Download Ch 8 - Algebra

©TeeJay Publishers
Homework for Level E book
Ch 8 - Algebra
Chapter 8
Algebra
Exercise 1
1.
Copy and simplify :(a) 8x + 4x
(b) 3y – 2y
(c) 9h + h
(d) 12p – p
(e) 5x + 3x + 4x
(f) 9w + 5w + w
(g) c + c + c
(h) 8k + 5k – 10k
(i) 15q + 9q – 19q
(j) 83d + 22d – 91d
(k) 20z – 17z + z
(l) 31h – 25h – 6h
(a) 18x + 14x – 27x
(b) 7y – y + 8y
(c) 12i + 7i – 14i
(d) 26t – t – t – t
(e) v + 11v + 4v – v
(f) 90j2 + 5j2 – j2
(g) h + 13h + 12h – 23h
(h) 7u + 6u – 12u
(i) 5g2 + 9g2 – 4g2
(j) 51e3 + 29e3 – 79e3
(k) z – 5z + 7z
(l) 31x – 35x – 6x
2. Copy and simplify :-
Exercise 2
1.
Write the number that comes out from these number machines :(a)
3
x
4
(c)
250
÷
50
1
?
(b)
8
20
?
(d)
10
+
+
5
– 21
?
+ (–5)
+
1
?
x
2. Write the number that must have gone in each time in these number machines :(a)
?
x
3
+1
13
(b)
?
x
(c)
?
÷8
+1
9
(d)
?
÷4
7
–2
26
+ (–4)
–3
3. Write an expression for each of the following :(a) y
multiply by 4
add 1
(b) t
multiply by 2
subtract 10
(c) b
multiply by 7
add 13
(d) x
multiply by 1
subtract from 5
divide by 2
subtract from h
(l)
s
add w
multiply by 14
subtract p
(n) 5 x
multiply by 21
(k)
k
(m) f
this is chapter 8
page 31
multiply by 51
subtract from i
©TeeJay Publishers
Homework for Level E book
Ch 8 - Algebra
Exercise 3
1.
2.
If a = 4 and b = 5, find the value of :(a) a + b
(b) a – b
(e) 8b ÷ 4
(i)
(d) 5a – 3b
(j) 4xy ÷ 20
(k) xy ÷ 40
(c) 5y + 2w
(d) 30 – 5z
(g) 2wx – 2
1
(k)
wz + x
3
(o) 2y – 5w + z
(h) 25 – 3yz
1
(l)
zw – xy
4
(p) 50 – 2wxyz
For w = 2, x = 3, y = 1 and z = 6, calculate :(a) 2w + 3 + x
(b) 1 + 2z – 2x
(e) z – 3w + y
(f)
w + 3x – y
(j)
2 x – 4 y + 2w
(i)
2z + 4y – x
(m) 10 – 2z + y
3.
7a ÷ 2
(c) ab
(n) 5 + 3yw– wzr
(a) Find an expression for the total cost of the items shown :(b) If s = 10 and t = 20, what is the total cost ?
4.
A regular decagon has side of length k cm.
(a) Find an expression for the perimeter.
(b) If k = 3, what is the perimeter ?
Exercise 4
1.
Copy each equation and solve :(a) x + 4 = 7
(b) y + 2 = 12
(c) 7 + y = 8
(d) p – 4 = 6
(e) 5 – x = 13
(f) 9 – w = 6
(g) c – 12 = 16
(h) 14 – g = 0
(i)
15 + e = 17
(j) 8 + x = 7
(k) z – 3 = –1
(l)
31 + a = –10
(a) 2a = 10
€
(d) 12p = 0
(b) 3y = 15
(c) 9h = 81
(e) 5x = 75
(f) 19w = 76
(g) 11z = 121
(h) 8k = 864
(i)
15q = 300
(j) 10k = 3000
(k) 20z = 6000
(l)
6h = 27
2. Copy and simplify :-
3.
Five calculators (c) are priced at £6.
(a) Form an equation in c to show this.
(b) Solve the equation to find the cost of one calculator.
this is chapter 8
page 32
©TeeJay Publishers
Homework for Level E book
Ch 8 - Algebra
Exercise 5
1.
Find the value of each variable by solving the equations :(a) 2x + 4 = 16
(b)
3y + 1 = 13
(c) 5y + 4 = 9
(d) 8p – 1 = 23
(e)
2x – 7 = 13
(f) 9 + 2w = 15
(g) 7c – 12 = 9
(h)
14 – 5g = 4
(i)
15 – 4e = –1
(j) 8 + 4x = 0
(k)
12z – 3 = 57
(l)
31 – 2a = –2
2. A rectangle with area 45 cm2, has length y cm and breadth 5 cm.
(a) Write an equation to show this information.
3. Solve :1
(a)
x=5
2
1
(d)
x+1=2
3
(b)
(e)
1
2
1
7
(b)
Solve the equation to find y.
y +3=7
(c)
z –3=0
(f)
1
2
1
h–5=9
10
k – 1 = –1
Exercise 6
1.
COPY the following as shown and place a “<“ sign or a “>“ sign between the numbers :(a) 5 ... 6
(b)
9 ... 5
(c) 0 ... –1
(d) –5 ... –1
(e)
2 ... –1
(f) –8 ... –11
(g) –4 ... 0
(h)
–6 ... –5
(i)
–22 ... –19
(j) –11 ... –10
(k)
–300 ... –200
(l)
16 ... 16 21
2. In this question you must choose x only from the numbers ..... {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 } :(a) x > 7
(b)
x<2
(c) x ≥ 9
(d) x ≤ 1
(e)
x>1
(f) x < 1
(g) x > 9
(h)
x≥0
(i)
x ≤ –1
3. In this question you must choose y only from the numbers, {–5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5} :(a) y > 2
(b)
y<1
(c) y ≥ –2
(d) y
€≤ 1
(g) y > –5
(e)
y > –1
(f) y ≤ –4
(h)
y < –5
(i)
y≥4
€
4. Solve these inequalities, using the numbers from –3 to 3 :(a) 4a > 8
(b)
3x < 3
(c) 5y ≤ 10
(d) 3g + 1 > 7
(e)
2x – 5 < –5
(f) 8 + 3x ≤ 8
this is chapter 8
page 33
©TeeJay Publishers
Homework for Level E book
Ch 8 - Algebra
Exercise 7
1.
Solve these inequalities, (leave your answer in form eg. x >3) :(a) x + 4 > 8
(b) x – 5 < 7
(c) 4 – h > 0
(d) 3f > 15
(e) 7w ≤ 28
(f) 3c ≤ 5
(g) 2x + 5 < 3
(h) 5y – 1 ≤ 9
(i) 3g – 1 > 14
(j) 4x – 6 < –6
(k)
1 + 3x ≤ 6
(l)
5y – 7 ≥ 7
2. Three pints of beer cost more than £4·50.
(a) Show this as an inequation.
(b) Solve to find the minimum cost of one pint.
3. Four bags of marbles and three extra
marbles weigh more than 17 grammes.
(a) Write an inequation to show this information.
(b) Solve to find the minimum weight of a bag.
Revision Exercise
1.
Simplify :(a) 8x + 4x
(b)
6y – 2y
(c) 5k + 2k – 4k
(d) 8d – 7d
(e)
w + 3w –2w
(f) 4h2 + 5h2 – 3h2
2. Write the unknown number :–
(a)
€
5
(c)
? €
x
3
+
6
x
6
+1
?
(b)
8
÷2
–5
31
(d)
?
÷3
+ (–1)
3. If s = 2, t = 3, u = 4 and v =5 find :(b) stu – 5v
(c) v 2 + u2 – (st)2
(b) y – 7 = 9
1
(e)
k = 16
2
(c) 2x + 1 = 11
1
(f)
y+1=3
5
(a) x + 4 > 10
(b) y – 1 < 9
(d) 2y ≤ 13
(e) 3k – 10 ≥ 0
(c) 3x ≤ 15
1
(f)
w+1 ≥ 5
2
(a) 3s + 2t + u – 2v
4. Solve :(a) x + 6 = 8
(d) 5h – 7 = 43
5. Solve :-
this is chapter 8
page 34
?
3