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Non-Calculator Paper: Track 1: Year 11

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These are the solutions to the Mathematics past questions for Non-Calculator Paper: Track 1: Year 11.
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(1.) Work out 50 ÷ 5


50 ÷ 5 = 10
(2.) Simplify this fraction to its lowest terms: $\dfrac{16}{56}$


$ \dfrac{16}{56} = \dfrac{16 \div 8}{56 \div 8} = \dfrac{2}{7} $
(3.) Anna has 6 boxes each containing 24 pencils.
How many pencils are there in all?


6 boxes @ 24 pencils per box = 6(24) = 144 pencils.
(4.) Sixty sweets are packed in bags.
Each bag contains 5 sweets.
How many bags are there?


Proportional Reasoning Method
bag sweets
1 5
what 60

$ what * 5 = 1 * 60 \\[3ex] what = \dfrac{60}{5} \\[5ex] what = 12\;bags $
(5.) A = (−2) × (−1) and B = 2 × (−1)
Fill in the box using < or >:
A $\boxed{\phantom{a}}$ B


A = (−2) × (−1) = 2
B = 2 × (−1) = −2
2 > −2
A > B
(6.) Circle the larger fraction. $$ \dfrac{3}{5} \;\;\;or\;\;\; \dfrac{11}{20} $$

$ \dfrac{3}{5} = \dfrac{3 * 4}{5 * 4} = \dfrac{12}{20} \\[5ex] \dfrac{11}{20} \\[7ex] \dfrac{3}{5} \gt \dfrac{11}{20} $
(7.) Work out the value of: 2.4 × 0.5


$ 2.4 * 0.5 \\[3ex] = \dfrac{24}{10} * \dfrac{5}{10} \\[5ex] = \dfrac{24 * 5}{10 * 10} \\[5ex] = \dfrac{120}{100} \\[5ex] = 1.2 $
(8.) Calculate the value of: $\dfrac{3}{10} \times \dfrac{5}{21}$


$ \dfrac{3}{10} * \dfrac{5}{21} \\[5ex] = \dfrac{3 * 5}{10 * 21} \\[5ex] = \dfrac{1 * 1}{2 * 7} \\[5ex] = \dfrac{1}{14} $
(9.) Simplify: $6a - 4b + 2a - 2b$


$ 6a - 4b + 2a - 2b \\[3ex] 6a + 2a - 4b - 2b \\[3ex] 8a - 6b $
(10.) Work out: (−24) ÷ (−6)


(−24) ÷ (−6) = 4
(11.) Ruth is going on a holiday to London.
She exchanges €400 into pounds (£).
How many pounds (£) does she get?

Number 11


Based on the Graph:
€ £
40 30
400 what?

40 × 10 = 400
∴ 30 × 10 = £300
(12.) Use π = 3 to work out the approximate value for the circumference of a circle radius 10 cm.


$ Circumference = 2 * \pi * radius \\[3ex] = 2(3)(10) \\[3ex] = 60\;cm $
(13.) A triathlon race consists of a swim, a run and a bicycle ride.

The swim is $\dfrac{1}{8}$ of the total distance.

The run is $\dfrac{2}{5}$ of the total distance.

What fraction of the total distance do the swim and run cover altogether?


$ \text{Let the total distance} = d \\[3ex] swim = \dfrac{1}{8}d \\[5ex] run = \dfrac{2}{5}d \\[5ex] swim + run \\[3ex] = \dfrac{d}{8} + \dfrac{2d}{5} \\[5ex] = \dfrac{5d + 16d}{40} \\[5ex] = \dfrac{21d}{40} \\[5ex] $ The fraction of the total distance that the swim and run cover altogether is $\dfrac{21}{40}$
(14.) Change 1.04 liters to ml.


$ \underline{\text{Unity Fraction Method}} \\[3ex] 1.04\;L * \dfrac{...mL}{...L} \\[5ex] = 1.04\;L * \dfrac{1\;mL}{10^{-3}\;mL} \\[6ex] = \dfrac{1.04}{0.001} \\[5ex] = \dfrac{1.04 * 1000}{0.001 * 1000} \\[5ex] = \dfrac{1040}{1} \\[5ex] = 1040\;mL $
(15.) Work out the value of a

2024: Number 15


$ a + 65^\circ + 45^\circ = 180^\circ ...sum\;\;of\;\;\angle s\;\;of\;\;a\;\;\triangle \\[4ex] a + 110 = 180 \\[3ex] a = 180 - 110 \\[3ex] a = 70^\circ $
(16.) Tina has €400.
She spends 35% of her money on a new bike.
How much does Tina spend on her new bike?


$ 35\% \;\;of\;\; 400 \\[3ex] = \dfrac{35}{100} * 400 \\[5ex] = 35(4) \\[3ex] = €140 $
(17.) Put a mark (✓) next to the regular quadrilateral.

Shape
parallelogram
rhombus
square
rectangle


A Regular Polygon is a polygon that is equilateral (equal sides) and equiangular (congruent angles).
The square has equal sides and congruent angles.
The regular quadrilateral in the table is the square.
(18.) Which fraction is equal to 20%?
$ \dfrac{1}{6} ~~~~~~~ or ~~~~~~~ \dfrac{1}{20} ~~~~~~~ or ~~~~~~~ \dfrac{1}{5} \\[5ex] $

$ \dfrac{1}{5} = \dfrac{1}{5} * 100\% = 20\% $
(19.) The area of this circle is 60 cm².
What is the area of the shaded part?

Number 19


The shaded area is one–quarter of the area of the circle.

$ \text{The shaded area} = \dfrac{1}{4} * 60 \\[5ex] = 15\;cm^2 $
(20.) There is $\dfrac{1}{4}$ of a cake left over in the fridge.
It is shared equally among Anne, Bill and Carl.
What fraction of the whole cake does Anne get?


$ \text{Let the entire cake} = c \\[3ex] Left\;\;over = \dfrac{1}{4}c \\[5ex] \text{Shared equally among 3 people} \\[3ex] \text{Each person gets:} \dfrac{1}{4}c \div 3 \\[5ex] = \dfrac{1}{4}c * \dfrac{1}{3} \\[5ex] = \dfrac{1}{12}c \\[5ex] $ Anna gets $\dfrac{1}{12}$ of the whole cake.




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