Find √(5.76)
A restaurant offers 2 starters: Soup (S) or Melon (M).
It offers 3 main courses: Beef (B), Fish (F), or Pasta (P).
List all the possible combinations of 1 starter and 1 main course.
It offers 3 main courses: Beef (B), Fish (F), or Pasta (P).
List all the possible combinations of 1 starter and 1 main course.
Worked Solution & Answer
List systematically starting with each item in turn, or multiply the number of choices for each stage together.
SB, SF, SP, MB, MF, MP
SB, SF, SP, MB, MF, MP
Answer: SB, SF, SP, MB, MF, MP
Luke wants to make a number machine so that y = 5x + 3
Here is his attempt.
Here is his attempt.
What mistake has he made?
Worked Solution & Answer
His machine gives (x + 3) × 5 = 5x + 15
To get 5x + 3, the machine must do × 5 first, then + 3. B1
To get 5x + 3, the machine must do × 5 first, then + 3. B1
Answer: Mistake He added 3 before multiplying by 5 instead of multiplying by 5 then adding 3
7 12 out of 16 squares shaded. What fraction of the shape is shaded in its simplest form?
What fraction of the shape is shaded?
Give your answer in its simplest form.
Give your answer in its simplest form.
Worked Solution & Answer
Solve the following linear equations.
(a) Solve 12 - e = 0 [1 mark]
e =
(b) Solve 7f = 0 [1 mark]
f =
Worked Solution & Answer
(a)
12 - e = 0 ⇒ e = 12 B1
Answer (a): e = 12
(b)
7f = 0 ⇒ f = 0 B1
Answer (b): f = 0
Two shops, Food Mart and Jim’s Store, both sell Kreemy Yoghurts.
At which shop are Kreemy Yoghurts the better value for money?
You must show all your working.
You must show all your working.
Worked Solution & Answer
Food Mart: 180p ÷ 5 = 36p per yoghurt M1
Jim’s Store: 105p ÷ 3 = 35p per yoghurt M1
Jim’s Store is better value. A1
Jim’s Store: 105p ÷ 3 = 35p per yoghurt M1
Jim’s Store is better value. A1
Answer: Jim’s Store (35p per yoghurt vs 36p at Food Mart)
In the diagram above, the expression in each block in the top two rows is found by using the following rule:
*The expression in any block is the sum of the expressions in the two blocks below it.*
Some expressions are already shown.
Use the rule to fill in the empty blocks in the diagram.
You must simplify your answers.
*The expression in any block is the sum of the expressions in the two blocks below it.*
Some expressions are already shown.
Use the rule to fill in the empty blocks in the diagram.
You must simplify your answers.
Fill in the three empty blocks with simplified expressions.
Worked Solution & Answer
1. Middle left block = (2x + 5) + (3x − 2) = 5x + 3. M1
2. Bottom right block: (3x − 2) + Block = 7x + 4 ⇒ Block = (7x + 4) − (3x − 2) = 4x + 6. M1
3. Top block = (5x + 3) + (7x + 4) = 12x + 7. A1
2. Bottom right block: (3x − 2) + Block = 7x + 4 ⇒ Block = (7x + 4) − (3x − 2) = 4x + 6. M1
3. Top block = (5x + 3) + (7x + 4) = 12x + 7. A1
Answer: Middle left block: 5x + 3; Bottom right block: 4x + 6; Top block: 12x + 7
Match each expression on the left with one on the right.
One has been done for you.
One has been done for you.
State the match for:
a + 3 × 2
a × 3 × 2
a × 3 + 2
a + 3 × 2
a × 3 × 2
a × 3 + 2
Answer
Worked Solution & Answer
a + 3 × 2 = a + 6 M1
a × 3 × 2 = 6a M1
a × 3 + 2 = 3a + 2. A1
a × 3 × 2 = 6a M1
a × 3 + 2 = 3a + 2. A1
Answer: Answer a + 3 × 2 = a + 6; a × 3 × 2 = 6a; a × 3 + 2 = 3a + 2
Batteries are sold in packs of 4, in packs of 8 and in packs of 12
A pack of 4 batteries costs £1.80
A pack of 8 batteries costs £3.20
A pack of 12 batteries costs £6.00
Which pack gives the best value for money?
You must show how you get your answer.
A pack of 8 batteries costs £3.20
A pack of 12 batteries costs £6.00
Which pack gives the best value for money?
You must show how you get your answer.
Worked Solution & Answer
Pack of 4: £1.80 ÷ 4 = 45p per battery M1
Pack of 8: £3.20 ÷ 8 = 40p per battery M1
Pack of 12: £6.00 ÷ 12 = 50p per battery → Pack of 8 gives the best value for money A1
Pack of 8: £3.20 ÷ 8 = 40p per battery M1
Pack of 12: £6.00 ÷ 12 = 50p per battery → Pack of 8 gives the best value for money A1
Answer: Pack of 8 (40p per battery vs 45p and 50p)
PQR is a straight line.
(i) Work out the value of x. [2 marks]
x =
(ii) Give a reason for your answer. [1 mark]
Worked Solution & Answer
(i)
x = 180 – 85 – 30 = 65 M1 A1
Answer (i): x = 65
(ii)
Angles on a straight line add up to 180°
Answer (ii): Angles on a straight line add up to 180°