Transcript Slide 1

Non Calculator Tests
Fourth Year
Non Calculator Tests
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Click on a number in the table above to go to the test of your choice.
The solutions follow after the test
Non Calculator – Test 1
Question
Solutions – Test 1
1
55
2
8¾
3
4½
4
1·8
5
10·08cm2
6
0·35
7
37.67
8
4
9
37·6
10
1¼
11
10√3
Non Calculator – Test 2
1. Find 8% of £24
2. Evaluate ½ of ( 12¼ - 5¾)
3. If a = 5 , b = -3 and c = 4 find the value of b2 – 4ac
4. Evaluate 2.9 + 3.1  2
5. Factorise 9x2 – 25
6. Solve 5(2x-1) = 7
7. The perimeter is 32 , find x
x
2x+1
8. Solve 2x2 = 98
9. If 5% of a number is 12 , find the number.
10. Solve the equations
x + y = 13
x –y=4
Question
Solutions – Test 2
1
₤1·92
2
3¼
3
-71
4
9·1
5
(3x-5)(3x+5)
6
x = 1·2
7
x=5
8
x = 7 or x = -7
9
240
10
x = 8.5 and y = 4.5
Non Calculator- Test 3
4
5
3
x

2
x
1. Evaluate
6x7
2. Evaluate 21.6 – 3.2 + 2.1
3. Find
1
3
of (
2
3
+
1
4
)
4. Write 60 as a surd in it’s simplest form.
5. Factorise fully 2x3 – 8x
6. Simplify 8 x  16
3x  6
Solve 5x – 2(3x-1) > 4
Remove the brackets (2x + 3)(x2 + x + 3)
If sinA = ¾ and A is an acute angle , find the exact
value of cosA.
10. If y varies directly as the cube of x and x is doubled ,
find the effect on y ?
7.
8.
9.
Question
Solutions – Test 3
1
x2
2
20·5
3
11/36
4
2√15
5
2x(x-2)(x+2)
6
8/3
7
x > 0·5
8
2x3 + 5x2 + 9x + 9
9
√7/4
10
multiplied by a factor of 8
Non Calculator- Test 4
1. If f(x) = 3 – 2x2 , find the value of f(-2)
2. Solve the equation 4x2 – 7x = 0
3. Factorise fully x3 – 4x
4 . Simplify 45 + 20
5
2
3
x

2
x
5. Simplify the expression
6 x 2
6. The perimeter of a rectangle is 36 and the
length is twice the breadth.
Find the area of the rectangle.
7. Solve
5
8
=
2
x
8. Find 3% of 480
1
9. Evaluate 3 2 1
2
7
10. Evaluate
16
3
4
Question
Solutions – Test 4
1
-5
2
x = 0 or x = 7/4
3
x(x-2)(x+2)
4
5√5
5
x9
6
72cm2
7
x = 3·2
8
14·4
9
7½
10
8
Non Calculator- Test 5
1. Find 25% of £19
2. If x = -2 and y = 5 find the value of
2
y
+x
x
3. If the diameter of the larger circle is
20cm and the diameter of the smaller circle is 10cm , find the shaded area.
Take as 3.
4. Subtract 6.38 from 13.9
5. How many pencils costing 14p
each can you buy for £5 ?

3 to a decimal.
5
18 in an English exam. What was his percentage mark.
7. A pupil scored
25
6. Change
8. Find the gradient of the line 2x+y+5 = 0
9. If y varies inversely as x and y=5 when x =2 find a formula connecting x and y.
Find y when x = 20.
10. If y = mx + c , change the subject of the formula to m.
Question
Solutions – Test 5
1
₤4·75
2
1·5
3
225cm2
4
7·52
5
35 pencils
6
0·6
7
72%
8
m = -2
9
y=10/x ; 0·5
10
m = (y-c)/x
Non Calculator – Test 6
5
find the exact value of cosx.
12
6
2. Write the fraction
with a rational denominator in its simplest
12
1. If tanx =
possible form.
3. Find 5% of 42
1
2 1
4. Evaluate 2 of   
 3 4
5. A rectangle has a length 3+2 and a breadth 3-2 .
Find an expression for the area in its simplest form.
6. Factorize 6x2 – 13x + 6
7. The perimeter of a square is 6cm. Find the area.
8. If x = 4 and y = 25 , find the value of
x
1
2

y

1
2
9. If f(x) = 3x + 5 and f(t) = 32 find the value of t
10. Solve the equation 3x2 = 5x
Question
Solutions – Test 6
1
12/13
2
√3
3
2·1
4
11/24
5
7
6
(3x-2)(2x-3)
7
2·25cm2
8
2/5
9
t=9
10
x = 0 or x = 5/3
Non Calculator – Test 7
5x 4  4 x 3
1. Simplify
10 x 2
2. Simplify
4 x 2  25
2x2  5x
3. Solve the equation 5 – 2(2x – 3)  13
4. If T =
4
( P  31) , change the subject of the formula to P
7
1
1
5. If x = 4 and y = 25 find the value of 2 x 2 y

2
6. If x + y = 17 and x – y = 4 , find the value of y.
7. If f(x) = 5x – 4 and f(t) = 11, find t.
8. Simplify  60 +  135
4
9. If A is an acute angle and sinA = , find the exact value of tanA.
10. Solve the equation 2x2 – 2x = 0 5
11. The diagram shows the graph of the function y = x2 – 4x.
Find the coordinates of point P
12. Find the equation of the straight line shown.

(4,7)
(0,5)
.
P
Question
Solutions – Test 7
1
2x9
2
(2x+5)/x
3
x less than or equal to -0·5
4
P = (7T-124)/4
5
4/5
6
y = 6·5
7
t=3
8
5√15
9
4/3
10
x = 0 or x = 1
Non Calculator – Test 8
1
2
1
2

1
2
1. Simplify 3x (2 x  x )
2. Find x as a surd in its simplest form.
6
2
x
3. If f(x) = 1 – 2x – x2 , find the value of f(-1).
4. If a = -3 , b = -2 and c = 5 find the value of b2 – 4ac.
5. The gradient of the line joining the points (2,5) and (5,t) is 3.
y
Find the value of t.
6. Find the coordinates of point T shown in the diagram
x–y=2
T
x
7. If x = 2 3 and y = 3 2 find the value of x2y2
x + y =10
8. The graph shows the relation  y varies inversely
as x’ . Find the equation connecting x and y.
9. If y varies directly as the cube of
x and x is doubled, find the effect on y.
10. Solve the equations 3x + 2y = 3
y = 2x – 9
11. Factorize fully 8x4 – 2x2
12. Remove the brackets (4x – 3)( x2 – 2x – 3)
.
(3,10)
Question
Solutions – Test 8
1
6x - 3
2
4√2
3
2
4
64
5
t = 14
6
T(6,4)
7
216
8
y=30/x
9
y is mult by factor of 8
10
x = 3 , y = -3
11
2x2(2x-1)(2x+1)
12
4x3 - 11x2 – 6x + 9
Non Calculator- Test 9
1.
2.
3.
4.
5.
What is the equation of the function shown in the diagram? 4
Factorize fully 15x2 + x – 6
If x = -4 , y = 2 and t = -3 find the value of yt – 2x2
Simplify  50 -  18
Simplify x 2  x  6
-4
x 2  3x
180
360
6. Evaluate 1 of ( 2  3 )
2
3
4
7. If y varies directly as the square of x and x is multiplied by a factor of 3
find the effect on y.
y
8 Find the equation of the straight line shown.
(4,6)

9 Write x as a surd in its simplest form.
10. Write as a single fraction
(16,0)
3x  1 1  2 x

2
3

11. If P  1 (3T  1) , change the subject to T and hence find T when P = 40.
2
12. Solve the inequation -5x –7  11
x
Question
Solutions – Test 9
1
4cos2x
2
(5x-3)(3x+2)
3
-48
4
2√2
5
(x+2)/x
6
17/24
7
y is mult. by a factor of 9
8
y = -0.5x + 8
9
4√5
10
(5x-5)/6
11
T=(2P-1)/3 ; T = 13
12
x greater than or equal to -3.6
Non Calculator- Test 10
1 Find the equation of the straight line shown in the diagram.
y
 (0,3)
2. If x = -2 find the value of 2x3.
3. Solve the equation 3x2 – 9x = 0.
(6,0) x
0
4. y varies inversely as the square of x and y = 1 when x = 2.
Find a formula connecting x and y. Find y when x = 4.
5. Evaluate
1 1
2 1
2 5
5
6. Simplify  75 -  48
2x+1
7. The perimeter of the rectangle shown is 62cm.
Make an equation and find x correct to 1 decimal place.
Continued on next slide
8.
Simplify
4
4x  8
9. Find 4% of £48
10. Multiply out the brackets (2x – 1)3
11. Write with a rational denominator
12. Simplify the expression
10 x 7  4 x 3
20 x 1
4
12
Question
Solutions – Test 10
1
y=-0.5x+3
2
-16
3
x= 0 , 3
4
y=4/x2 , y = 0.25
5
3
6
√3
7
x = 7.5
8
1/(x-2)
9
₤1·92
10
8x3 – 12x2 + 6x -1
11
√3/2
12
2x11
Non Calculator - Test 11
1. Write down the equation of the trig. function shown in the diagram.
3
90º
1
2. If A is an acute angle and sinA = ,
find the exact value of cosA giving 2
your answer as a surd with a rational denominator.
-3
x2  9
3. Simplify the fraction
x 2  3x
7
4. Find the exact value of cosA
A
5
5. Remove the brackets
(5-3x)(6-4x)
6. If x = 36 and y = 9 find the exact value of
1
2
x y
1
2
8
360º
5x + 2y = 17 and 3x –2y = 7.
7.
Find x if
8.
Find the gradient of the line shown in the diagram.
9.
Simplify the expression shown
1
2

1
2
x (x  x )
10. Find 25% of 47
12. If f(x) =
1 1 1
 
2 3 4
3x
and f(t) = 1
2
2x  1

(-5,0)
x
(0,-4)
1
2
11. Evaluate
y
, find t.
Question
Solutions – Test 11
1
3sinx
2
√3/2
3
x3
x
4
1/7
5
30 – 38x + 12x2
6
18
7
x=3
8
m = -0·8
9
x – x-1
10
11·75
11
7/12
12
t=¼
Non Calculator – Test 12
3
1. Identify the trig. graph shown in the diagram
2. Factorize fully 8x2 – 2y2
5. Evaluate
360º
-3
2
x
3. If x = -10 and y = -4 find the exact value of
as an improper fraction in its simplest form.
y3
4. Write as a single fraction
180º
3x 1  x

2
3
1
1
3
of (12  7 )
2
4
4
6. If f(x) = 1 - 2x - 4x2 , find the value of f(-3).
giving your answer
7. The area of a square is 300cm2.
Find the perimeter giving your answer as a surd in its simplest form.
8. Find the equation of the straight line shown.
(0,4)
0
9. y varies directly as the square root of x and y = 5 when x = 16.
Find an equation connecting x and y. Find y when x = 9.
10. Evaluate (5x2)3
11. Solve the equation 7x – 4x2 = 0.
12. Multiply out the brackets and simplify
(3 2 +1)(2 2 – 1)
(12,0)
Question
Solutions – Test 12
1
3sin2x
2
2(2x-y)(2x+y)
3
-25/16
4
11x  2
6
5
2¼
6
-29
7
P = 40√3
8
m = -1/3
9
y=1.25√x ; y = 3.75
10
125x6
11
X = 0 , 7/4
12
11 - √2
Non Calculator - Test 13
1. The rectangle shown has an area of 84 sq.cm
Make an equation and find x.
3
2. Factorize fully 25t3 – t
3. Find 25% of £350
4. Simplify the expression x(x-3) – (x+2)(x+1)
5. Evaluate 13.8 – 15.6 + 4.7
6. If f(x) = 3x2 – 2x –1 , find the value of f(-2).
7. Write 500 as a surd in its simplest form.
2x+3
8. Find the gradient of the straight line shown.
(0,5)
0
9. y varies directly as the square of x and y = 40 when x = 2.
Find an equation connecting x and y. Find y when x = 3.
10. Evaluate (yx3)4
11. Solve the equation x2 – 6x - 16 = 0.
12. Multiply out the brackets and simplify ( 2 +1)( 2 – 1)
(10,0)
Question
Solutions – Test 13
1
x = 12·5
2
t(5t-1)(5t+1)
3
₤87·50
4
-6x -2
5
2·9
6
15
7
10√5
8
m = -½
9
y = 10x2 , y = 90
10
y4x12
11
x = 8 , -2
12
1
Non Calculator – Test 14
1. If sinx =
5
13
, find the exact value of cosx.
2. Write the fraction
6
with a rational denominator in its simplest possible form.
18
3. Find 9% of 36
4. If f(x) = 3x – 5 and f(t) = 22 , find t.
5. A rectangle has a length 5+6 and a breadth 5-6 .
Find an expression for the perimeter in its simplest form.
6. Factorise 9x2 – 12x + 4
7. The perimeter of a square is 14cm. Find the area.
8. If x + y = 24 and y = 2x , find the value of y
9. Simplify
9 x  18
10 x  20
10. Solve the equation x2 = 3x
Question
Solutions – Test 14
1
12/13
2
√2
3
₤3·24
4
t=9
5
20
6
(3x-2)(3x-2)
7
12·25
8
16
9
9/10
10
x=0,3
Non Calculator – Test 15
2
5
5
x

4
x
1. Simplify
20 x 1
2. Simplify
x 2  25
x 2  5x
3. Solve the equation 5x – (2x – 3)
4. If W =
1
( M  2)
2
1
, change the subject of the formula to M.
5. If x = 9 and y = 16 find the value of
1
2
x y

6. Find the V.A.T. on an article costing £400.
7. If f(x) = 5x – 1 and f(t) = -6 , find t.
1
2
8. Simplify  20 +  45
9. If A is an acute angle and sinA =
1
, find the exact value of tanA.
2
10. Solve the equation 2x2 + 5x = 0
11. The diagram shows the graph of the function y = x2 – 6x.
P
Find the coordinates of point P, the minimum value of the function.
 (10,2)
12. Find the equation of the straight line shown.
(0,1)

Question
Solutions – Test 15
1
x8
2
x5
x
4
2
3
M = 2W - 2
5
¾
6
₤70
7
t = -1
8
5√5
9
1
3
3
x
10
x = 0 or x = -5/2
11
(3,-9)
12
y = 0.1x + 1
Non Calculator – Test 16
1. Find 3% of £78
2. Evaluate
1 1 1
 
2 3 5
3. If a = 2 , b = -1 and c = 3 find the value of ab – bc
4. Evaluate 12  4 + 6  2
5. Factorise fully 2x2 – 3x + 1
6. Simplify the algebraic fraction
x2  9
x 2  4x  3
7. Write 56% as a fraction in its simplest form.
8. Solve the equation 2x2 + 5x = 0
9. If 10% of a number is 17 , find the number.
10. Find the value of x if x + y = 12 and x – y = 11
11. y varies inversely as x and y = 6 when x = 5. Find y when x = 10.
Question
Solutions – Test 16
1
₤2·34
2
19/30
3
1
4
15
5
(2x-1)(x-1)
6
(x-3)/(x+1)
7
14/25
8
x = 0 or x = -5/2
9
170
10
x = 11·5
11
y=3
1. Evaluate
Non Calculator – Test 17
x3  x6
x 2
2. Evaluate 1.6 – 3.2 + 2.1
3. Write
2x  1 x  1
as a single fraction

3
4
4. Write 80 as a surd in it’s simplest form
5. Factorize fully 6x2 – 13x + 6
6. Find the gradient of the line which
passes through the points (0,4) and (4,0)
7. Solve 6x – (3x+2) < 4
8. Remove the brackets (x + 1)(x2 + x - 3)
2
9. If sinA =
, and A is an acute angle , find the exact value of tanA.
3
10.
If y varies directly as the square of x and x is trebled ,
find the effect on y ?
Question
1
2
Solutions – Test 17
x11
0·5
3
4
5
(5x+7)/12
4√5
(3x-2)(2x-3)
6
7
8
m = -1
x<2
x3 + 2x2 – 3x - 3
9
10
2/√5
y is mult. by a factor of 9
Non Calculator – Test 18
1. Write the number 32.6904 correct to
a) 1 decimal place b) 5 significant figures
2. Write the fraction
possible form.
12 with a rational denominator in its simplest
18
3. Find 50% of 6.42
4. If f(x) = 1-2x and f(t) = 5 , find t.
5. Factorize fully 4x3 – 4x
6. Make x the subject of the formula y = mx + c.
7. The area of a square is 400cm2. Find the perimeter.
8. If x = 4 and y = 16, find the value of
9. Simplify (x+1)2 – x(x-2)
10. Solve the equation 5 – 2(x-2) = 0
x
3
2

y

1
2
Question
1
2
Solutions – Test 18
a) 32·7 b) 32·690
2√2
3
4
5
3·21
t = -2
4x(x-1)(x+1)
6
7
8
x = (y-c)/m
P = 80
9
10
½
4x + 1
x = 4·5
Non Calculator – Test 19
3
2
1
2

1
2
1. Simplify 2x ( x  2x )
2. Find x as a surd in its simplest form.
8
4
x
3. If f(x) = x – x2 , find the value of f(-2).
4. Find 9% of £44
5. The gradient of the line joining the points (0,2) and (2,t) is 4.
Find the value of t.
6. Write 40% as a fraction in its simplest form.
7. If x = 4 3 and y = 3 3 find the value of 2xy
8. Solve the inequation 4x – 2(1-2x) > 5
9. If y varies directly as the square of x and x is doubled, find the effect on y
10. Solve the equations 3x + 2y = 16 ,
11. Factorize fully x4 – 81
y=x–2
12. Remove the brackets (x – 3)(2x2 – 2x + 3)
Question
1
2
Solutions – Test 19
2x2 – 4x
4√3
3
4
5
6
-6
₤3·96
t = 10
2/5
7
8
9
72
x>7/8
y is mult. by 4
10
11
12
x=2
(x-3)(x+3)(x2+9)
2x3 – 8x2 + 9x - 9
Non Calculator – Test 20
1. Find the equation of the straight line with a gradient
3 which passes through the origin.
2. If x = -2, find the value of 3x2.
3. Solve the equation x2 + x = 0.
4. y varies inversely as the square of x and y = 2 when x = 2.
Find a formula connecting x and y. Find y when x = 4.
5. Evaluate 2 1  1 3
4
5
6. Simplify  125 +  75
7. The perimeter of the rectangle shown is 70cm.
Make an equation and find x correct to 1 decimal place.
4
x+6
8. Simplify
2
2x  4
9. Find 2% of £48.50
10. Multiply out the brackets (x + 2)3
11. Write
2
8
in its simplest form with a rational denominator
12. Simplify the expression
20 x 6  4 x 3
16 x 2
Question
1
2
3
4
5
Solutions – Test 20
y = 3x
12
x = 0 or x = -1
y=8/x2 ; y = ½
6
5(√5 + √3)
7
8
9
10
11
12
x = 25
1/(x-2)
₤0·97
x3+ 6x2 + 12x + 8
√2/2
5x11
3
3
5
Non Calculator 21
1. Find 10% of £19
2. If x = -1 and y = -2 find the value of
3. Solve the equation x2 = 3x.
y
3
+ x
x
4. Subtract 4.8 from 7.3
5. Remove the brackets (x + 2) (x2 + x + 1)
6. Write 8% as a fraction in its simplest form.
7. Simplify
2x  4
3x  6
8. Find the gradient of the line 2x+4y+1 = 0
9. If y varies inversely as the square of x and y=2 when x =3
find a formula connecting x and y. Find y when x = 6.
10. If C =
5
( F  32)
9
, change the subject of the formula to F.
Question
1
2
3
4
5
6
7
8
9
10
Solutions – Test 21
₤0·19
1
x=0,3
2·5
x3+3x2 + 3x + 2
2/25
2/3
m = -½
x = 6 and y = ½
F
(9C  160)
5
Non Calculator – Test 22
1. If sinx = 8 and x is an acute angle, find the exact value of cosx.
17
2. Write the fraction
possible form.
6
18
with a rational denominator in its simplest
3. Find 2% of 80
1 1
1
4. Evaluate
of   
2 4
4
5. A rectangle has a length 32 and a breadth 52
Find an expression for the area in its simplest form.
6. Factorise x2 – x – 6
7. The perimeter of a square is 10cm. Find the area.
8. If x = 9 and y = 4 , find the value of 4
x
1
2
y

1
2
9. If f(x) = 2x + 5 and f(t) = 23, find the value of t.
10. Solve the equation x2 = 5x + 4
Question
1
2
Solutions – Test 22
15/17
√2
3
4
5
6
2
3/16
30
(x-3)(x+2)
7
8
9
6·25cm2
6
t=9
10
x=4,x=1
Non Calculator – Test 23
x 5  12 x 4
1. Evaluate
6x7
2. Evaluate 11.6 – 13.2 + 2.5
3. Remove the brackets (x + 2)(2x2 –x -1)
4. Calculate the gradient of the line which passes
through the points (5,2) and (-3,2).
5. If f(x) = 3 – x – x2, find the value of f(-3).
2
x
x
6. Simplify
x 1
7 . Solve the equation x2 = 7x
8 . Simplify √45 + √20 - √125
9 . If P = 4(L + B), change the subject of the formula to B.
10 . If y varies inversely as the square of x and x is doubled,
find the effect on y?
Question
1
2
Solutions – Test 23
2x2
0·9
3
4
5
2x3 + 3x2 – 3x -2
m=0
-3
6
7
8
x
x=0,x=7
0
9
10
B=(P-4L)/4
y is divided by a factor of 4
Non Calculator – Test 24
6
360º
90º
1. Write down the equation of
the trig. function shown in the diagram.
-6
2
2. If A is an acute angle and sinA =
, find the exact
3
value of tanA, giving your
answer as a surd with a rational denominator.
3. Simplify the expression
2x(x+1) – (2x+1)(x-1)
5
4. Find the exact value of cosA.
5. Solve the equation 2 x  1
3

x5 4
A
2
6. If x = 25 and y = 4, find the exact value of x -½ y ½
4
7. Solve 2x + 3y = 21 , y = 3x – 4
8. Find the equation of the line shown in the diagram.
y

(-2,0)
9. Simplify the expression shown
1
2
4 x (x
(0,-1)

1
2
1
2
x )
10. Find 15% of 20
11. Evaluate
x
1 2 3
 
4 3 4
12. Write √120 as a surd in its simplest form.
Question
1
2
3
4
5
6
7
8
9
10
11
12
Solutions – Test 24
6sinx
2/√5
3x + 1
37/40
x = -3·8
2/5
x=3,y=5
y = -0·5x - 1
4 – 4x
3
3/4
2√30
Non Calculator – Test 25
1. Find 5% of £60000
2. Evaluate ¼ of ( 10½ - 4)
3. A square has an area of 400 cm2. Find the perimeter of the square.
4. Evaluate 1.52 + 2.52
5. Factorize fully x3 – x
6. Solve 4 – 2(x – 1) = 9
7. If f(x) = x2 + 1 find the value of f(-2) – f(2).
8. Write as a surd with a rational denominator
8
20
9. A discount of 40% is offered on a television set in a
sale. Find the sale price of the set.
10. State the gradient of the line with equation x + 4y = 1
Question
1
2
Solutions – Test 25
₤3000
3
4
5
80cm
8·5
x(x-1)(x+1)
6
7
8
9
x = -1·5
0
4√5/5
Needs a price for the set.
10
-¼
9
1
16
Non Calculator – Test 26
1. Simplify
1
2
1
2

1
2
8x (0.5x  x )
Find the value of this expression when x = 4.
x
2. Find x as a surd in its simplest form
2
8
3. If f(x) = 10 – x – x3 , find the value of f(-1).
4. y varies directly as x and y =6 when x = 4. Find y when x = 10.
5. Solve the equation x3 – 4x = 0
y
x–y=1
6. Find the coordinates of point
P
x
x+y =8
7. If x = 4 2 and y = 5 2 find the value of x3y
8. The graph shows the relation  y varies inversely as the square of x
Find the equation connecting x and y
9. If x = 4, find the value of
√(x2 +
48)
 (2,5)
10. Find the point where the line 2x + 3y -12 = 0 cuts the x axis
11. Factorize fully
x2 – x – 12
12. Remove the brackets (x – 3)( x2 – 2x + 3)
Question
1
2
Solutions – Test 26
4x - 8
2√15
3
4
5
12
y = 1·5x ; y =15
x = 0,2,-2
6
7
8
9
P(4.5,3.5)
1280
y=20/x2
8
10
(6,0)
11
12
(x-4)(x+3)
x3 - 5x2 + 9x - 9
Non Calculator – Test 27
5x 4  2 x 3
1. Simplify
10 x 1
2. Simplify
x 2  25
x 2  6x  5
3. Solve the equation 15 – (2x – 3)
4. If M =
2
(T  12)
3
1
, change the subject of the formula to T
5. Write as a single fraction
2x  1 x  1

5
3
6. If 2x + y = 11 and x – y = 4 , find the value of y.
7. If f(x) = x2 – 4 and f(t) = 32, find t.
8. Simplify  242 -  98
9. If A is an acute angle and cosA = 12 ,
13
find the exact value of tanA.
10. Solve the equation x2 – 11x = 0
11. The diagram shows the graph of the
function y = x2 – 6x. Find the coordinates
of point P
6
P
12. Find the gradient of the straight line
shown.

(5,9)
(0,3)
Question
1
2
Solutions – Test 27
x8
3
4
x  8.5
5
x5
x 1
T
3M  24
2
x2
15
6
7
8
9
y=1
t = 6 , -6
4√2
10
11
12
x = 0 , 11
(3,-9)
tan A 
6
5
5
12
Non Calculator – Test 28
1. Find 5% of £1800
2y
2. If x = -2 and y = -4 , find the value of
+
x
3. A straight line has equation 4x + 3y = 24.
Find the point where the line cuts the y axis.
4. Subtract 4.76 from 12.38
5. Simplify the algebraic fraction
6. Change
2
to a decimal.
5
10 x  30
20 x  60
x3
28
7. A pupil scored 40 in a Mathematics exam.
What was his percentage mark?
8. If f(x) = ax2 + 5 and f(2) = 33, find the value of a.
9. If y varies inversely as the cube of x and y = 1 when x =2.
Find a formula connecting x and y. Find y when x = 1.
10. If e = mc2 , change the subject of the formula to c.
Question
1
2
3
Solutions – Test 28
90
-4
(0,8)
4
5
6
7·62
7
8
9
70%
a=7
,x=1,y=8
10
½
0·4
y
8
x3
C
e
m
Non Calculator – Test 29
1. Find the equation of the straight line shown in the diagram.
y
 (0,4)
2. If x = -1, find the value of x3 – x2
0
3. Solve the equation 4x2 – 81 = 0.
4. P varies directly as the square of Q and P = 1 when Q = 2.
Find a formula connecting P and Q.
Find P when Q = 10.
5. Evaluate 4 1  11
2
3
6. Simplify  200 -  128
(8,0) x
7. The perimeter of the rectangle shown is 56cm.
Make an equation and find x.
6
2
8. Evaluate
, when x = 2
5x  8
9. Evaluate 100 – 25

3x+4
5
10. Multiply out the brackets (1-3x)(4x+1)
11. Write with a rational denominator
12. Simplify the expression
x3
2 x 2
4
2 1
Question
1
2
3
Solutions – Test 29
m = -½
-2
9/2 and -9/2
4
5
6
P=¼Q2 , P = 25
6
2√2
7
8
9
x=6
1
-25
10
11
12
1 + x – 12x2
4(√2 – 1)
½x5
Non Calculator – Test 30
12
1. What is the equation of the function shown
in the diagram?
180
-12
2. If f(x) = 4 + ax3 and f(-1) = 5 , find a formula for f(x)
and hence find the value of f(3)
3. If x = 10 , y = -2 and t = 3, find the value of
4. Simplify 3x4
5. Simplify
6. Evaluate

(2x2)3
x2  x  6
x 2  3x
1
3 7
of (  )
4
4 4
7. If x + y = 20 and y = 4x , find the value of y.
x y
t
360
y
8. Find the equation of the straight line shown.
(1,3)

(5,0)
9. Write x as a surd in its
simplest form.
x
x
4
6
10. Evaluate 23.2 – 34.7 + 16.8
11. If
3
L  (3M  5) , change the subject to M and hence find M when L=10.
2
12. Solve the inequation -2x +9
 5
Question
1
Solutions – Test 30
12cos2x
2
3
4
a = -1; f(3)=-23
4
24x10
5
6
(x-2)/x
5/8
7
x = 4 , y = 16
8
9
10
11
y = -0.75x + 3.75
x = 2√5
5·3
M=(2L-15)/9
x  2
12
Non Calculator – Test 31
1. The rectangle shown has an area of 72 sq.cm
Make an equation and find.
2. Factorize fully
121x4
–
x2
2x
4x
3. Find 8% of £300.
4. Simplify the expression 2x(x-3) – (x+2)(2x+3)
5. Evaluate 1.42
6. A Doctor has been given a pay rise of 25%.
He now earns ₤60000 per annum.
How much did he earn before the pay rise.
7. Write 800 as a surd in its simplest form.
8. Find the gradient of the straight line shown.
(0,6)
0
(12,0)
9. If x = √5 + 2 and y = √5 – 2, find the value of x2 + y2.
10. Evaluate √(122 + 52)
11. Solve the equation 121 – x2 = 0
12. Multiply out the brackets and simplify
(3 7 +1)( 7 – 1)
Question
1
Solutions – Test 31
x =3
2
3
4
5
x2(11x-1)(11x+1)
₤24
-13x - 6
1·96
6
7
8
48000
20√2
m = -½
9
10
11
18
13
x = 11 , -11
12
20 - 2√7
Non Calculator – Test 32
1. A straight line passes through the points (2,0) and (0,-2).
Find its equation.
2. Solve the equation 3x  2 Give your answer correct to
4 3
1 decimal place
3. Factorize fully 4x2 – 15x + 9
4. y varies inversely as the square of x and x is doubled.
Find the effect on y.
3
4
3
11
5. Evaluate 2  1
6. Simplify  32 -  18
7. The perimeter of the rectangle shown is 50cm.
Make an equation and find x correct to 1 decimal place.
5
8. Simplify
8
16 x  8
2x+1
9 Find 3% of £1000
10. If x = -5, y= 4 and t = -2 , find the value of x2yt.
11. Write
6
12
in its simplest form with a rational denominator.
12. Simplify the expression (x+1)2 – x(x+1)
Question
1
2
3
4
5
6
7
8
9
10
11
12
Solutions – Test 32
y=x-2
x = 0·9
(4x-3)(x-3)
y is divided by 4
3½
√2
x = 9·5
1/(2x-1)
₤30
-200
√3
x+1
Non Calculator – Test 33
1 Evaluate
y2  y5
y 1
2. Simplify the expression -4x(x-1) – 4x(1-x) 3
x x 1

3
5
Write 72 as a surd in its simplest form.
Factorize fully x2 – 16x + 64
3. Write as a single fraction
4.
5.
6. The point (t,5) lies on the line x + y - 9 =0. Find the value of t.
7.
8.
9.
Solve the inequation 5x – (3x-2) < - 4
Remove the brackets (2x + 1)(x2 - x - 10)
A car costs ₤24000. In a sale it is reduced by 20%.
Find the sale price of the car.
10 A car travels a distance of 250 km in 2½ hours.
Calculate the average speed of the car in km per hour.
Question
1
2
Solutions – Test 33
y8
0
3
4
(2x+3)/15
6√2
5
6
(x-8)(x-8)
t=4
7
8
9
x < -3
2x3 – x2 – 21x - 10
₤19200
10
100km/hr
Non Calculator – Test 34

3
2
3
2
1
2
1. Simplify x ( x  x )
2. Find x as a surd in its simplest form.
10
5
3. If P = 2(L+B), change the subject to L.
4. Find
x
3
of 75
5
5. State the gradient of the line with gradient y = 4.
6. Write 60% as a fraction in its simplest form.
7. If x = 4 3 and y = 3 3 find the value of xy2
8. Solve the equation x(x+1) = x2 + 10x + 18
a
9. The point (4,2) lies on the curve with equation y  2
x
Find the equation of the curve.
10. Evaluate 8.4 – 11.2 – (-7.8)
11. Factorize fully x4 – 9x2
12. Remove the brackets (x + 1)(x2 – x - 3)
Question
1
Solutions – Test 34
1 – 1/x
2
3
4
5
5√3
L=(P-2B)/2
45
m=0
6
7
8
3/5
108√3
x = -2
32
x2
5
x2(x+3)(x-3)
x3 – 4x - 3
9
10
11
12
Non Calculator – Test 35
1. The rectangle shown has a perimeter of 70 cm.
Make an equation and find x.
x
2. Factorize fully 8x2 +2x – 15
2x+5
3. Find 75% of £360
4. Simplify the expression
5. Write as a single fraction
x 2  36
x 2  6x
4
3

x x 1
6. If f(x) = x2 – 5x –6 , find the value of f(-3).
7. Write
12
as a surd in its simplest form with a rational denominator.
20
8. Find the gradient of the straight line shown.
(0,6)
0
(16,0)
9. y varies directly as the cube of x and y = 64 when x = 4.
Find an equation connecting x and y. Find y when x = 6.
10. Simplify (2y3x4)3
11. Solve the equation x2 = 6x
12. Multiply out the brackets and simplify
(3 2 +1)(2 2 + 1)
Question
1
2
3
4
Solutions – Test 35
x = 10
(4x-5)(2x+3)
₤270
5
x6
x
x4
x( x  1)
6
18
7
8
9
10
6√5/5
-3/8
y = x3 , y = 216
8y9x12
11
12
x=0,6
13 + 5√2
Non Calculator – Test 36
1.5
1. Write down the equation
of the trig. function shown in the diagram.
360º
90º
-1.5
1
2. If A is an acute angle and tanA = 3
,
find the exact value of cosA , giving your answer as a
surd with a rational denominator.
2
x
3. Simplify the fraction
x2  x
6
4. Find the exact value of cosA in the diagram shown.
5
4
5. If f(x) = x3 -7 and f(t) = 57, find t.
A
1
2
6. If x = 49 and y = 9 , find the exact value of x  y
3
2
7. Find x if
x + y = 17 and x – y = 8.
8. Find the equation of the line shown in the diagram.
y

(-2,0)
x
(0,-1)
1
2
1
2

1
2
9. Simplify the expression shown
x (4 x  2 x )
evaluate this expression when x = 3.
10. Find 125% of 40
1
2
1 1
3 7
11. Evaluate 1  2 
12. If f(x) =
x and f(t) = 1 , find t.
2
x 1
. Hence
Question
1
2
3
4
5
6
7
8
9
10
11
Solutions – Test 36
1.5sinx
3/√10
x/(x+1)
1/8
t=4
189
x = 12·5
y = -0·5x - 1
4x – 2 ; 10
50
12
t=1
1
5
6