ABC Education · 11+ Practice

Week 38 · Maths Practice Paper

11 questions · 80 marks · Suggested time: 1 hour.

Question 1

[4 marks]

When we multiply three consecutive numbers as shown below we obtain the following answer

12 × 13 × 14 = 2184

Using this result, work out the answers to these four questions

(a)

12 × 13 × 28 =

(b)

6 × 13 × 14 =

(c)

120 × 130 × 140 =

(d)

218478 =

Question 2

[5 marks]

The average weight of four apples is 150g. A fifth apple, weighing 130g, joins the group.

(a)

Find the new average weight of the group.

(b)

Two more apples, weighing X and Y, join the group. The new average weight of all seven apples is 148g. If X = 152g, how heavy is Y?

Question 3

[5 marks]

A cafe's loyalty scheme gives points for the size of drink bought: Large = 3 points, Medium = 2 points, Small = 1 point. For example, a customer buying 15 Large, 9 Medium and 6 Small drinks earns 15×3 + 9×2 + 6×1 = 69 points.

Complete the missing numbers below using the point totals given. Nadia's row needs an extra fact: she bought an EQUAL number of each size.

(a)

Toby bought 11 Large, 7 Medium and ? Small, earning 54 points. How many Small drinks?

(b)

Fern bought 12 Large, ? Medium and 5 Small, earning 55 points. How many Medium drinks?

(c)

Milo bought ? Large, 6 Medium and 4 Small, earning 46 points. How many Large drinks?

(d)

Nadia bought an equal number of each size and earned 42 points. How many of each size did she buy?

Question 4

[5 marks]

In a puzzle, every letter stands for a whole number, and the value of a word is the product of the values of its letters. No letter in this puzzle has the value 1.

(a)

If DOO = 32, find the values of D and O.

(b)

Using those values, if DOG = 56, find G.

(c)

Work out the value of the word GOD.

(d)

If the word MEGA = 210, work out the value of the word GAME.

Question 5

[5 marks]

A delivery company charges a fixed handling fee plus an amount for every 500g of a parcel's weight (the WHC, Weight Handling Charge). For example, with a fixed fee of GBP 2 and a WHC of 60p, a 1kg parcel costs 2 + 2 × 0.60 = GBP 3.20.

(a)

At another company the WHC is 90p and the total charge for a 1.5kg parcel is GBP 7.20. What is the fixed fee?

(b)

At a third company the fixed fee is GBP 1.80 and the total charge for a 2.25kg parcel is GBP 6.30. What is the WHC?

Question 6

[6 marks]

A company called BrightBox makes rectangular tins. For every tin, the depth is always 1.5 times its width. For example, a tin with width 6cm has depth 6 × 1.5 = 9cm.

(a)

Find the depth of a tin if its width is 8cm.

(b)

Find the width of a different tin if its depth is 45cm.

(c)

Find the depth of a third tin if the perimeter of one of its faces (measured using its width and depth) is 50cm.

Question 7

[8 marks]

The height, h, in metres, reached by a firework after t seconds, launched with power rating P, is given by the formula:

h = P × t²4

(a)

Find the height reached by a firework with power rating 12 after 2 seconds.

(b)

Find the height reached by a rocket with power rating 5 after 1 minute.

(c)

A firework reaches 108m in 6 seconds. What is its power rating?

(d)

A firework with power rating 16 reaches 196m. How long does this take?

Question 8

[8 marks]

At 'The Sandwich Hut', a sandwich costs GBP 2.50, a drink costs GBP 1.20 and a snack costs GBP 0.80. Last Friday lunchtime they sold 60 sandwich-and-drink deals, 45 sandwich-and-snack deals, and 30 drinks on their own.

(a)

Work out their total income that lunchtime.

(b)

The owner paid GBP 0.90 for each sandwich sold and GBP 0.30 for each drink sold, and GBP 25 in total for snack ingredients. How much did the food she sold that lunchtime cost her?

(c)

She employs one member of staff for GBP 9 per hour, working 4 hours, and other costs were GBP 8. What are the TOTAL costs?

(d)

How much profit did she make that lunchtime?

Question 9

[10 marks]

The table below shows the first three rows of a table with three columns. The values on each row are the same, expressed in different forms.

Row 1: 1 | 1 | 1²
Row 2: 1+3 | 4 | 2²
Row 3: 1+3+5 | 9 | 3²
Row 4: 1+3+5+7 | (a) | (b)
Row 5: (c) | 25 | (d)
Row 6: 1+3+5+7+9+11 | (e) | -

(a)

Row 4, middle column

(b)

Row 4, right column

(c)

Row 5, left column

(d)

Row 5, right column

(e)

Row 6, middle column

Question 10

[10 marks]

Maya has 12 cards numbered 1 to 12. Five of her friends each pick two of the cards.

The numbers on Priya's two cards multiply to give 24
One of Ravi's cards is double the other
The numbers on Sam's two cards are both square numbers
The difference between the numbers on Zoe's two cards is 7
The numbers on Emma's two cards multiply to give 132

(No card is used by more than one friend.)

Priya

Which two cards?

Ravi

Which two cards?

Sam

Which two cards?

Zoe

Which two cards?

Emma

Which two cards?

Question 11

[14 marks]

The firm GlowTech makes components called Glow-Tubes, which can be joined in two ways. In a SERIA, the two values are simply added: SERIA(5, 8) = 13. In a PARLA, the values are combined by adding fractions and inverting the result, e.g. PARLA(4, 12): 14 + 112 = 412, so PARLA(4, 12) = 3.

(a)(i)

SERIA(9, 6) =

(a)(ii)

PARLA(8, 24) =

(b)

SERIA of 15 and PARLA(9, 18) =

(c)

Triple PARLA(4, 12, 6) =

(d)

Triple PARLA(20, 30, ?) = 4. Find the missing value.

(e)

PARLA(3, 7) = ? (this one is not a whole number!)