Free Printable IST Year 10 Mathematical Underpinnings

1.

33 = 4a - 7

a)

a=-10

b)

a=10

c)

a=4.5

2.

-3a + 8 = 14

a)

a= -2

b)

a= -7.5

c)

a= 2

d)

a= 6

3.

3 + (¹∕₄)a = 31

a)

a= 28

b)

a= 112

c)

a= 7

d)

a= 67

4.

0 = 8z + 8

a)

-1

b)

1

c)

0

d)

8

5.

8v - 4(v + 8) = 8

a)

2

b)

10

c)

4

d)

-4

6.

2x - 3 + 4x = 27

a)

12

b)

4

c)

5

d)

15

7.

-11 + 3(b + 5) = 7

a)

1

b)

-1

c)

3

d)

-3

8.

-(n - 8) = -2

a)

6

b)

10

c)

-10

d)

-6

9.

Solve.
(2x - 3) / 4 = 9

a)

x = 24

b)

x = 12

c)

x = 17.5

d)

x = 19.5

10.

Solve the equation:
^x/₃+ 10 = 15

a)

75

b)

15

c)

25

d)

5

11.

12x = 144

a)

x = 12

b)

x = 4

c)

x = 2

d)

x = 132

12.

3y = -15

a)

-5

b)

5

c)

-3

d)

3

13.

-4x + 1 = 21

a)

x=120

b)

x=5

c)

x=30

d)

x=-5

14.

-6x = 18

a)

3

b)

-3

c)

6

d)

-6

15.

5 = 7s - 9

a)

2

b)

6

c)

7

d)

8

16.

2b = -16

a)

8

b)

4

c)

-8

d)

3

17.

4a + 3 = 15

a)

2

b)

4

c)

1

d)

3

18.

52 = -5x - 3

a)

x = 11

b)

x = -11

c)

x = 275

d)

x = -275

19.

-30 - 5x = 120

a)

x = 18

b)

x = -18

c)

x = 30

d)

x = -30

20.

Which equation has x = 2 as a solution?

a)

3 + x = 10

b)

11 + x = 13

c)

4x = 32

d)

5x =25

21.

Factor
4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

22.

Factor
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

23.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

24.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

25.

Factor
2x² - 13x - 70

a)

(2x-7)(x+10)

b)

(7x+5)(x+2)

c)

(2x+7)(x-10)

d)

2(x+7)(x+10)

26.

Factorise completely

15ab - 3b

a)

5a (3b - 3b)

b)

3b (5a - 1)

c)

3b (5a)

d)

5a (3b)

27.

Factorise completely

4px + 5xy - 7x

a)

x (4 - 5y - 7x)

b)

x (4p + 5y - 7)

c)

x (4p - 5y + 7x)

d)

x (4p - 5x - 7y)

28.

Factorise completely

4h - h (54k + 18)

a)

2 (27 - 7k)

b)

h (-27 + 7k)

c)

2h (27k + 7)

d)

-2h (27k + 7)

29.

Factorise completely

2abp + 8ab - 8abp

a)

2ab (4 - 3p)

b)

ab (4 - 3p)

c)

b (4 +3p)

d)

ab (-4+3p)

30.

Factorise completely

7c (a + 2b) - 4c (2b + a)

a)

3c (a + 2b)

b)

11c (a + 2b)

c)

a + 2b

d)

c (a - 2b)

31.

Expand and simplify: (4x + 3)(5x + 6)

a)

20x² + 39x + 18

b)

20x² + 9x + 18

c)

20x² + 18

d)

20x² – 18

32.

Expand and simplify:
(5h + 4k)²

a)

25h² + 40hk + 16k²

b)

25h² + 40h + 16k²

c)

25h² + 40hk - 16k²

d)

25h² - 40hk + 16k²

33.

(3pr + 7)(3pr – 7)

a)

9p²r² - 49

b)

9p²r² + 49

c)

9p²r² - 42pr + 49

d)

9p²r² - 42pr - 49

34.

Factorise completely

15ab - 3b

a)

5a (3b - 3b)

b)

3b (5a - 1)

c)

3b (5a)

d)

5a (3b)

35.

Factorise completely

4px + 5xy - 7x

a)

x (4 - 5y - 7x)

b)

x (4p + 5y - 7)

c)

x (4p - 5y + 7x)

d)

x (4p - 5x - 7y)

36.

Factorise completely

4h - h (54k + 18)

a)

2 (27 - 7k)

b)

h (-27 + 7k)

c)

2h (27k + 7)

d)

-2h (27k + 7)

37.

solve for y

y - x = 5

a)

y = 5 + x

b)

y = -5 - x

c)

y = -5 + x

d)

y = 5 - x

38.

solve for R

pV = nRT

a)

R= pV/nT

b)

R= p/n + V/T

c)

R= pV - nT

d)

R= (pV-n)/T

39.

solve for y

-2 = 4x + y

a)

y = -2 + 4x

b)

y = 2 - 4x

c)

y = -2 - 4x

d)

y = 2 + 4x

40.

Solve for y

x = 3y - 24

a)

y = (x + 24)/3

b)

y = x/3 + 24

c)

y = 3x + 24

d)

y = 3(x + 24)

41.

Solve for y

5x - 3y = -9

a)

y = 5/3x - 3

b)

y = 5/3x + 9

c)

y = 5/3x + 3

d)

y = 3/5x + 3

42.

Solve for y

y+8=4x

a)

y = 4x + 8

b)

y = -4x - 8

c)

y = -4x + 8

d)

y = 4x - 8

43.

Solve for y

-4x + 2y = -6

a)

y = -2x + 3

b)

y = 2x + 3

c)

y = 2x - 3

d)

y = -2x - 3

44.

Solve for y

y - 5x = 11?

a)

y = -5x + 11

b)

y = -5x - 11

c)

y = 5x + 11

d)

y = 5x

45.

Solve for y

2y + 4x = 12

a)

y = -4x + 12

b)

y = -4x + 6

c)

y = -2x + 6

d)

y = -2x + 4

46.

Solve for y

-3y + 6x = 12

a)

y = 2x + 4

b)

y = 2x - 4

c)

y = -2x + 4

d)

y = -2x - 4

47.

S = 3F - 24 Solve for F

a)

F = (S + 24)/3

b)

F = S/3 + 24

c)

F = 3S + 24

d)

F = 3(S + 24)

48.

Solve for y:
8x + 4y= 16

a)

y = -8x + 16

b)

y = 2x -4

c)

y = -2x + 4

d)

y = -8x + 12

49.

Solve for y:
5x - y = 16

a)

-y = 5x + 16

b)

y = 5x + 16

c)

x = 5y - 16

d)

y = 5x - 16

50.

Solve m - n = 5 for m.

a)

m = 5 + n

b)

m = -5 - n

c)

m = -5 + n

d)

m = 5 - n

51.

Solve -2 = 4r + s for s.

a)

s = -2 + 4r

b)

s = 2 - 4r

c)

s = -2 - 4r

d)

s = 2 + 4r

52.

IR = V
(solve for R)

a)

R = IV

b)

R = ^I/_V

c)

R = ^V/_I

d)

R = V - I

53.

Solve:
y = mx + b , for b

a)

y - mx = b

b)

y + mx = b

c)

^y/_mx = b

d)

y + mx = -b

54.

Solve for x.
z = xy

a)

x = ^z/_y

b)

x = ^y/_z

c)

x = yz

d)

y = xz

55.

Solve for s.
r = 2s - 8

a)

s = r + 2

b)

s = r/2 + 4

c)

s = r + 8 2

d)

s = 2r + 16

56.

Solve:
4x + 2y = 1 , for y

a)

y = -2x + ½

b)

y = 2x - ½

c)

y = 2x + ¼

d)

y = -2x + ¼

57.

Solve:
C = 2πr, for r

a)

C/(2π) = r

b)

C + 2π = r

c)

C - 2π = r

d)

2πC = r

58.

Solve:
a - b - c = 9 , for a

a)

a = b + c + 9

b)

a = b - c + 9

c)

a = -b + c + 9

d)

a = -b - c + 9

59.

Solve:
C = xv + x , for v

a)

(C-x)/x = v

b)

(C+x)/x = v

c)

(-C-x)/x = v

d)

(Cx)/x = v

60.

What should we do first to solve for x?
y=mx+b

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

61.

Rearrange the Following Equations to the format "y=mx+b"
-4x+y=12

a)

y= -4x + 12

b)

y= 4x + 12

c)

y= -4x - 12

d)

y= 4x - 12

62.

Rearrange the Following Equations to the format "y=mx+b"
1/2x + y = 3/4

a)

y= -1/2x + 3/4

b)

y= -1/2x - 3/4

c)

y= 1/2x + 3/4

d)

y= 1/2x - 3/4

63.

Rearrange the Following Equations to the format "y=mx+b"
2.5x - y = 19

a)

y= -2.5x - 19

b)

y= 2.5x - 19

c)

y= -2.5x + 19

d)

y= 2.5x + 19

64.

Rearrange the Following Equations to the format "y=mx+b"
4x + 3y = 24

a)

y= -4/3x - 8

b)

y= -4/3x + 8

c)

y= 4/3x + 8

d)

y= 4/3x - 8

65.

Rearrange the Following Equations to the format "y=mx+b"
3x - 5y = 15

a)

y= 3/5x - 3

b)

y= -3/5x - 3

c)

y= -3/5x + 3

d)

y= 3/5x + 3

66.

Solve for "m"
2m - 7 = 15 + 0m

a)

100

b)

25

c)

11

d)

8

67.

Solve for "m"
-5m + 4 = 64 + 0m

a)

25

b)

11

c)

-12

d)

-8

68.

Solve for "m"
18m - 21 = 15m + 3

a)

8

b)

-8

c)

11

d)

25

69.

Solve for "m"
2m - 54 = -1m + 21

a)

100

b)

25

c)

11

d)

8

70.

Solve for "m"
_{-12m + 2 = -15m + 5}

a)

1

b)

-1

c)

2

d)

0

71.

Solve for x.
5(x + 1) = 5x + 2

a)

x = 5

b)

x = 1

c)

No solution

d)

Infinite solutions

72.

Solve for x.
3x + 2 = 6x - 7

a)

x = 9

b)

x = 3

c)

x = -3

d)

x = 7

IST Year 10 Mathematical Underpinnings

Total questions: 72

Worksheet time: 3hrs 2mins

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