Inequalities (Calculator allowed) Name:
1) Complete the boxes with one of the inequality symbols, >, <, ≥ or ≤ to make the mathematical statement correct.
2
a)
4
x > 2 therefore -x
c)
-2
(1)
b)
(1)
d)
-3
-4
(1)
x ≤ 0 therefore x2
0
(1)
4
2 a) This diagram shows the inequality x ≤ -1
-5
Draw a diagram to express the inequality
0 ≤ 𝑥 ≤ 4 using the scale provided
-4
-3
-5
-4
-3
-4
-3
-2
-2
-2
-1
0
-1
1
0
2
1
3
2
4
3
5
4
6
5
7
6
7
8
8
(2)
b) Use inequalities to describe each of the diagrams.
i)
-5
ii)
-4
-3
-2
-1
0
1
2
3
4
5
6
7
-5
8
……………………………………………………………….
(1)
iii)
-5
-1
0
1
2
3
4
5
6
7
8
…………………………………………………………….
(1)
iv)
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
-5
……………………………………………………………….
(2)
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
…………………………………………………………….
(2)
8
3 a) The graph below shows y = 3
b) On the graph below, shade the region which
satisfies both inequalities; x ≥ 0 and y ≤ -1
Use the graph to shade the region y ≥ 3
y axis
5
y axis
5
4
4
3
3
2
2
1
x axis
1
x axis
-4
-3
-2
-1 0
-1
1
2
3
4
5
-4
6
-3
-2
-1 0
-1
1
2
3
4
5
6
-2
-2
-3
(1)
-3
(3)
y axis
5
c) Here is a graph with shaded regions.
Tick the inequalities below which describe the shaded region.
4
3
y≥𝒙
𝒚≤𝒙
2
1
x≥𝟒
𝒙≤𝟒
𝒚≥𝟏
𝒚≤𝟏
© t.silvester 2017
1: 8
2: 16
-4
-3
-2
(2)
3: 24 4: 32 5: 40 6: 48 7: 56
-1 0
-1
x axis
1
2
3
4
5
6
-2
-3
6
Page total:
Inequalities (Calculator allowed)
4) Solve the inequalities
a) 3m – 2 < 7
Answer: …………………………. (2)
b) 2a – 3 ≥ 3a + 1
Answer: …………………………. (2)
c) -6 ≤ 2p < 4
Answer: …………………….……. (2)
6
5) Mr Parker wants to organise a skiing trip. He needs at least 9 students in order for the trip to go ahead.
The hotel he would like to book can take a maximum of 18 students
a) Express the number of students n that can go on the skiing trip using inequalities.
…………………………………………………………………………………………………………………………………………………………
(1)
b) Each student is allowed to take spending money. Mr Parker advises that students may each take from €50 to
€150 to spend. Every student gives Mr Parker their spending money to look after. Express the total amount of
spending money (€x) that Mr Parker looks after as inequalities.
……………………………………………………………………………………………………………………………………………………………………
………...………………………………………………………………………………………………………………………………………...…
(3)
4
6 a) Colin is wondering about the smallest possible value and the biggest possible value that would round to 40
when rounded to the nearest 10. He expresses his answer using inequalities 35 ≤ 𝑥 ≤ 39.
Explain why he is wrong.
………………………………………………………………………………………………………………………………………………...............
…………………………………………………………………………………………………………………………………………………………
(1)
b) For each of the following, express the upper and lower bounds using inequalities.
i) 800 rounded to the nearest 100
……………………………………………………………………………………………
……………………………………………………………………………………………
ii) 0.09 rounded to the nearest hundredth
……………………………………………………………………………………………
……………………………………………………………………………………………
iii) 45 000 rounded to 2 significant figures
(1)
(1)
……………………………………………………………………………………………
……………………………………………………………………………………………
(2)
5
© t.silvester 2017
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Inequalities (Calculator allowed)
7) The area of the rectangle is 20 cm2, rounded to the
nearest 10. The length is 5 cm, rounded to the nearest unit.
Work out the maximum width, x, of the rectangle.
Not drawn to scale
Area ≈ 20 cm2
x cm
Approx. 5 cm
………………………………………………………………………………………………………………………………………………...............
………………………………………………………………………………………………………………………………………………...............
………………………………………………………………………………………………………………………………………………...............
…………………………………………………………………………………………………………………………………………………………
Answer:
……………………………………….
cm (3)
3
y axis
9
8 a) The grid shows a shaded region bounded by 3
inequalities. The first inequality has been written
for you. Write the two other inequalities which
form the shaded region.
8
7
6
…………………………………………………………………………………….
5
…………………………………………………………………………………….
4
3
…………………………………………………………………………………….
2
Answer: y ≥ 0
………………………...
……….………………..
(4)
1
0
0
1
2
3
4
5
6
7
8
9
10
x axis
y axis
b)
A shaded region is described by the inequalities
x > -4,
y+x<2
and
2y = x – 2.
Show the shaded region clearly on the set of axes provided.
……………………………………………………………………………
x axis
……………………………………………………………………………
……………………………………………………………………………
……………………………………………………………………………
…………………………………………………………………
8
(4)
9) Matt is sending a parcel from Jersey to Australia. The parcel must first travel from Jersey to England and then
from England to Australia. There are weight (w) restrictions for each stage in the journey. To send the parcel by
parcel post to England from Jersey, the weight must satisfy the inequality; 2𝑘𝑔 < 𝑤 ≤ 7𝑘𝑔. To send the parcel
by parcel post to Australia from England, the weight must satisfy the inequality; 2𝑘𝑔 ≤ 𝑤 < 9.5𝑘𝑔. Write
inequalities to describe the weight restrictions for the whole journey.
…………………………………………………………………………………………………………………………………………...............
© t.silvester 2017
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(2)
2
Inequalities (Calculator allowed)
10 a) The diagram shows the graph of y = x2 + 5x + 4
Use the graph to work out the solution to the
inequality x2 + 5x + 4 < 0
y axis
Answer: ……………………………………………………… (2)
b) Henry gives the solution to a different quadratic
inequality as 𝑥 ≤ −2 𝑎𝑛𝑑 𝑥 ≥ 3
Write down the inequality that Henry has solved.
x axis
……………………………………………………………………
…………………………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………………………….
Answer:
……………………………………………………………………….
(3)
5
11) Solve the following inequalities by factorising. You must show full working.
a) y (y – 3) > 10
Answer: ……………………………….. (3)
b) 3m2 – m – 8 ≤ 0
Answer: ……………………………….. (3)
c) 5b2 + b – 6 < b2 – b
Answer: ……………………………….. (3)
9
© t.silvester 2017
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