Year 7 Progress Test Practice Worksheet Solutions

Prime Numbers

Prime numbers are numbers that have only two factors: 1 and themselves. From the list provided (9, 27, 3, 2, 6, 15, 100, 19), the prime numbers are 3, 2, and 19.

Factors of 27

Factors of a number are the numbers that divide evenly into that number. The factors of 27 from the list provided are 9, 27, and 3.

Digital Time (24-Hour Clock)

a) 9:35 am - 09:35
b) 12:35 pm - 12:35
c) 12:35 am - 00:35

Attendance Analysis

To arrange the seasons in order of attendance from lowest to highest, we sort the attendance numbers:

2011/2012: 7528
2010/2011: 7645
2008/2009: 7887
2007/2008: 8311
2009/2010: 9287

Decrease in attendance from 2009/2010 to 2010/2011:
$9287 - 7645 = 1642$

Roman Numerals

MMXI = 2011
MMIV = 2004

MMXI (2011) was made more recently than MMIV (2004).

Fractions on a Decimal Number Line

Placing fractions on a decimal number line requires converting them to decimals:

$\frac{1}{8} = 0.125$
$\frac{2}{4} = \frac{1}{2} = 0.5$
$\frac{1}{5} = 0.2$

Perimeter Calculation

Given: Perimeter (P) = Formula and x = 3m, y = 5m.
If the perimeter of the shape is 32m, we need to find the values of 'x' and 'y'. Without the formula, we cannot calculate but assuming a rectangle P = $2x + 2y$

If P = 32, then $2x + 2y = 32 \implies x + y = 16$. Many solutions exist such as x = 8 and y = 8. We cannot determine with the context provided.

Iron Rod Lengths

Data: 73, 74, 74, 75, 75, 75, 76, 76, 77, 77, 78, 78, 79, 79, 80

(a) Median: The middle value of the sorted data. Since there are 15 values, the median is the 8th value, which is 76.

(b) Mode: The value that appears most frequently. In this data set, 75 appears three times, which is more than any other number. So, the mode is 75.

Missing Angle

Missing angle problems requires an image, which has not been provided. Angle questions are usually found using facts like:

• Angles on a line add up to 180 degrees.

• Angles in a triangle add up to 180 degrees.

• Angles around a point add up to 360 degrees.

• Knowing types of triangles (isosceles, equilateral, scalene).

• Parallel lines.

Ratio Problem

There are 10 girls in the athletics club. The ratio of girls to boys is 5:4.

Let the number of boys be $b$. Then:

$\frac{10}{b} = \frac{5}{4}$

Cross-multiply:

$5b = 40$

$b = 8$

There are 8 boys.

Pie Chart Angles

Total students = 120

• Chicken: 13 students, 39 degrees

• Cheese: 55 students, 165 degrees

• Cheese and tomato: 32 students, 96 degrees

• Salad: 20 students, ? degrees

To find the angle for salad, we can set up a proportion:

$\frac{20}{120} = \frac{x}{360}$

$x = \frac{20 \times 360}{120} = \frac{7200}{120} = 60$

The angle for salad is 60 degrees.

Special Offer Calculation

Normal prices of the books: £4, £3.80, £3, £1.20
The cheapest book is £1.20, and it's free.
Total normal price: $4 + 3.80 + 3 + 1.20 = 12$
The fraction of the normal total price he saves is $\frac{1.20}{4 + 3.80 + 3 + 1.20} = \frac{1.20}{12} = \frac{1}{10}$

So, the correct calculation is:

$\frac{1.20}{4 + 3.80 + 3 + 1.20}$

Angle Calculation

To calculate the size of angles ‘a’ and ‘b’, additional information or a diagram is needed. Without a visual representation or further context, it's impossible to determine the values of ‘a’ and ‘b’.

Spinner Game

With two spinners each having numbers 1, 2, 3, 4, the total scores range from 2 to 8.
Listing the sums from the table:
2: (1,1)
3: (1,2), (2,1)
4: (1,3), (2,2), (3,1)
5: (1,4), (2,3), (3,2), (4,1)
6: (2,4), (3,3), (4,2)
7: (3,4), (4,3)
8: (4,4)
Least likely to most likely:
2 (1 way)
8 (1 way)
3 (2 ways)
7 (2 ways)
4 (3 ways)
6 (3 ways)
5 (4 ways)

Table Pattern Completion

Pattern: Each increase in the number corresponds to an increase in the number of sticks.
1 -> 8
If we consider the number of sticks to be $s$ and the number in the pattern to be $n$, then:

If $n = 1$, $s = 8$

If $n = 2$, we need to determine $s$ from the image which is not present.

Without additional info, we can't do this question.

Solving Equations

a) $\frac{3}{5} + \frac{2}{4} = \frac{3}{5} + \frac{1}{2} = \frac{6}{10} + \frac{5}{10} = \frac{11}{10} = 1\frac{1}{10}$

b) $3\frac{1}{5} + 4\frac{3}{5} = 7\frac{4}{5}$

c) 60% as a fraction: $\frac{60}{100} = \frac{3}{5}$
60% as a decimal: 0.6

d) $3.22 \times 0.4 = 1.288$

e) $22.5 \div 1.5 = 15$

Circumference Calculation

Diameter (d) = 13cm

Circumference (C) = $\pi d$

$C = \pi \times 13 \approx 40.84$

Rounded to the nearest whole centimeter, the circumference is 41 cm.

Jam Problems

a) Regular jam: 55% of 340 grams is sugar.

$0.55 \times 340 = 187$

There are 187 grams of sugar in a 340-gram jar of regular jam.

b) Low sugar jam: 102 grams of sugar in a 340-gram jar.

$\frac{102}{340} \times 100 = 30$

The percentage of sugar in her low sugar jam is 30%.

Sports Club Ratio

Total people = 15

Ratio of females to males = 2:3

Total ratio parts = $2 + 3 = 5$

Each part represents: $\frac{15}{5} = 3$

Females: $2 \times 3 = 6$
Males: $3 \times 3 = 9$

There are 6 females and 9 males in the club.

Map and Distance

To answer questions related to the map and distances between villages, the actual map is needed which has not been supplied.

Triangle Angles

a) To calculate the size of angle 'a': Need information about the relationships of other angles to determine 'a'.
b) To calculate the size of angle 'b': Need information about the relationships of other angles to determine 'b'. PS is a straight line, adjacent angles will sum to $180^{\circ}$

Area of a Triangle

Base = 8cm

Height = Not provided, so the question can't be solved.

The area (A) of a triangle is: $A = \frac{1}{2} \times base \times height$