..
Diagnostic self-test
This test is only meant as a guide to what we need to work on during the exercise periods. 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
3. a)
5.
6.
7.
8.
(
b)
4. a)
c) 3(-7)
h) 6-8
)
b)
e) 3 – (-7)
d) 3-7
c)
c)
d)
e)
3(-8)-1 + 5(-2)-3
Multiply: a) (3+t)(7-t)
b) (2c + 5d)2
Simplify 3(t-3) – 2(t-1)2 + 2(t+1)2
Multiply and simplify: (4x2 + 3x -7)(4x – 3)
Solve for x:
9. 10x -5 + 6 - 2x = 3x – 14
10. a) 3.7x + 8.4 = 15.8
11. a)
b)
c) 2x2 = 162
b)
=0
Simplify when possible and calculate:
12. a)
b)
, b≠2 and a≠0
d)
g)
, x≠1
, x, y ≠0
c)
, x≠-2 f)
e)
, x≠-1/2
13. The function f is defined by f(x) = 3x2 + 2x -1. Calculate
a) f(1)
b) f(0.5)
c) f(y)
d) f(4t)
(Answers on page 2)
1
, b≠2
Answers
1. a) 21
b) -10
c) -21
d) -4
e) 10
f) 4
g) 5
2. -16
3. a) 17/30
b) 77/54
c) 5
4. a) ½
b) 2
c) 1/3
d) 0
e) ½
5. -1
6. a) 21 + 4t – t2
b) 4c2 + 20cd + 25d2
7. 11t - 9
8. 16x3 – 37x + 21
9. x = -3
10. a) x = 2
b) x = 2
11. a) x = 5
b) x = 1
12. a) 15
h)
13. a) 4
b) -2
c) x =± 9
c) 4x3
i)
b) 0.75
e) –a2
f) 3
x
2x
(NOT
)
2x  1
x 1
c) 3y2+2y-1
d) 48t2+8t-1
2
h) 2