Diagnostic self-test
This test is only meant as a guide for repetition of maths you did at school. It is not an
examination.
Calculate (without using a calculator):
1. a) (-3)(-7)
b) (-3) - 7
f) 8-4
g) -5
3
4
2. (-2) + (-1) – (-3)2
1
2
1
3. a) 2 + 5 − 3
3 1
−
6
1
+
3 2
4. a) 42
b)
b)
14
9
2−
8
9
2
c) 3(-7)
h) 6-8
1
− (27 + 18)
2
9
c)
5+18
c)
−4+8
1 1
+
2 3
5
2
e) 3 – (-7)
d) 3-7
2−(5−2)
− 1 − 3+(−1)(−1)
−4
d)
4
− −2
2
e)
(−2)(5−3)
(7−15)
5. a) You buy 4 kg (kilograms) of apples and pay SEK 60. What is the price of one kg?
b) You buy 300 grammes = 3/10 kg of cherries. You pay SEK 15. What is the price of
one kg?
c) Did you use the same method in a) and b)? If not, how can two different methods be
correct when the problems have the same structure?
6. 3(-8)-1 + 5(-2)-3
7. Multiply: a) (3+t)(7-t)
b) (2c + 5d)2
8. Simplify 3(t-3) – 2(t-1)2 + 2(t+1)2
9. Multiply and simplify: (4x2 + 3x -7)(4x – 3)
10. Multiply and simplify (2x3+3x2-5x+2)(2x2+3x-4)+(3x-5)(4x2-2x+3)
Solve for x:
10. 10x -5 + 6 - 2x = 3x – 14
11. a) 3.7x + 8.4 = 15.8
12. a)
𝑥+1
𝑥−3
b)
𝑥−1
8𝑥
9
−5𝑥
−2=
6
+
13
9
c) 2x2 = 162
= 3 b)𝑥+3=0
Simplify when possible and calculate:
13. a)
d)
25
9
5
÷ 27
48𝑎(2−𝑏)
27𝑎3
÷
b)
(2𝑥−2)
, x≠1
(1−𝑥)
16(𝑏−2)
9𝑎4
, b≠2 and a≠0
c)
e)
4𝑥 2 𝑦 3
2𝑥 3
∙
16𝑥 4
8𝑦 3
6𝑥+12
2𝑥+4
2𝑥
14. The function f is defined by f(x) = 3x2 + 2x -1. Calculate
b) f(0.5)
c) f(y)
d) f(4t)
(Answers on page 2)
1
𝑏+1
5𝑏
, x≠-2 f) 3𝑏−6 + 𝑏−2 , b≠2
g) 2𝑥+1, x≠-1/2
a) f(1)
, x, y ≠0
Answers
1. a) 21
b) -10
c) -21
d) -4
e) 10
f) 4
g) 5
h) 2
2. -16
3. a) 17/30
b) 77/54
c) 5
4. a) ½
b) 2
c) 1/3
5. a)
60
4
= 15
10
b) 15 ∙
3
d) 0
e) ½
= 50
c) To divide by a quotient (3/10) is the same as to multiply by its inverse (10/3).
6. -1
7. a) 21 + 4t – t2
b) 4c2 + 20cd + 25d2
8. 11t - 9
9. 16x3 – 37x + 21
10. 4x5+12x4+3x3-49x2+45x-23
11. x = -3
12. a) x = 2
b) x = 2
13. a) x = 5
b) x = 1
14. a) 15
f)
16𝑏+1
3(𝑏−2)
15. a) 4
b) -2
c) x =± 9
c) 4x3
g)
b) 0.75
d) –a2
e) 3
x
2x
(NOT
)
2x  1
x 1
c) 3y2+2y-1
d) 48t2+8t-1
2