Year 7 Mathematics
Algebraic Techniques Practice Test 1
Name__________________________
1. a) List the individual terms in the expression 5a + b + 14c .
b) State the coefficient of each pronumeral in the expression 5a + b + 14c .
c) Give an example of an expression with exactly two terms, one of which is a
constant term.
2 Write an expression for each of the following.
a) 3 more than a
b) 5 less than m
c) the sum of a and b
d) double the value of y
e) the product of a and b
3. Write an expression for each of the following without using the x or ÷ symbols.
a) a is halved, then 6 is added
b) the sum of a and b is taken and then divided by 3
c) the sum of a and one-third of b
d) 7 is subtracted from y and the result is tripled
4 Given that a = 5, evaluate:
10
a) a + 7 b) 8a c) +4−a
a
5 Substitute x = 4 and y = 7 to evaluate these expressions.
a) 5x + y + 8 b) 80 – (2xy + y )
6 If p = 4 and t = 5, find the value of:
a) 3p2 b) t2 + p3 c) p 2 + 32
7 Which two of these expressions are equivalent: 3x + 4, 8 – x , 2x + 4 + x ?
8 Which of the following pairs are like terms?
a) 3a and 2a b) 3b and 3c c) 2ab and 5ba d) 4k and k e) 2a and 4ab
9 Simplify the following by collecting like terms.
a) 7b + 2 + 3b
b) 12d – 4d + d
c) 5 + 12a + 4b – 2 – 3a
d) 13a + 8b + 2a – 5b – 4a
e) 12uv + 7v – 3vu + 3v
10 Write 4 x a x b x c without multiplication signs.
11 Simplify 4a x 2b x 3c, giving your fi nal answer without multiplication signs.
12 Simplify 3w x 4w.
13 Write (2a + 1) ÷ 3 without a division sign.
8ab
14 Simplify the expression
12b
15 Expand the following expressions.
a) 5(x + 3)
b) 8(a – 4)
c) 3(a + 2b)
d) 5a(3p – 7q)
Answers
1. a) 5a, b, 14c .
b) coefficient of a is 5 coefficient of b is 1 coefficient of c is 14 .
c) An example is 2a + 7 you could a different example – check
2. a) a + 3
b) m – 5
c) a + b
d) 2 x y
e) a x b
a
3. a) +6
2
a+b
b)
3
b
c) a +
3
d) 3(y – 7)
4 a) 12 b) 40 c) 1
5 a) 35 b) 17
6 a) 48 b) 89 c) 5
7 3x + 4 and 2x + 4 + x ?
8 a) yes b) no c) yes d) yes e) no
9 a) 10b + 2
b) 9d
c) 5 + 9a + 4b + 3
d) 11a + 3b
e) 9uv + 10v
10 4abc
11 24abc
12 12w2.
2a +1
13
3
2a
14 Simplify the expression
3
15 Expand the following expressions.
a) 5x + 15
b) 8a – 32
c) 3a + 6b
d) 15ap – 35aq