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Drawing, Solving & Mixed Models! 📐✏️
1. Solve the following equation: 2(x + 3) = 14
Hint: Expand the brackets first!
2. Draw the inequality x ≥ 2 on the blank number line below.
Remember: Use a closed circle because it is 'greater than or equal to'.
3. Write down the \textbf{smallest integer} (whole number) that satisfies the inequality x > 5.
1. Calculate the area of a trapezium with parallel sides of 10 cm and 14 cm, and a height of 5 cm.
2. On the dotted grid below, carefully sketch a rectangle that has a total area of exactly 12 cm².
(Assume the distance between each dot is 1 cm).
3. Write down the base and height of the rectangle you just drew.
1. A bag contains 3 red counters and 2 blue counters. What is the theoretical probability of picking a red counter? (Write as a fraction).
2. Ayosh flips a fair coin. Mark with an 'X' on the probability scale below the chance of the coin landing on 'Tails'.
3. The probability that it will rain tomorrow is 0.15. What is the probability that it will NOT rain?
1. Find the Volume of a cuboid with a length of 5 cm, a width of 4 cm, and a height of 10 cm.
2. Sketch the net of a cube in the blank space below.
Hint: A cube has 6 square faces. You can draw the "cross" shape net!
3. If one side of a cube is 3 cm, calculate the area of just one face.
1. I am thinking of a number, n. Write an inequality to show:
"Double the number is at least 20."
Hint: "At least" means greater than or equal to.
2. Solve this inequality: 3x - 2 < 10
3. Look at the inequality on the number line. Write the correct inequality for x.
1. Convert 40 kilometres to miles.
2. Solve the equation with unknowns on both sides:
5x + 2 = 2x + 17
1. Sophia spins a spinner 50 times in an experiment. It lands on the colour RED 20 times. What is the experimental probability of the spinner landing on RED? (Simplify your fraction).
2. Shade the blank circle below to create a spinner where the theoretical probability of landing on a shaded section is exactly 1/4.
3. The theoretical probability of rolling a '6' on a normal dice is 1/6. If a dice is rolled 60 times and lands on '6' exactly 30 times, is the dice fair? Explain.
1. The three interior angles of a right-angled triangle are x°, 2x°, and 90°. Construct an equation and solve it to find x.
2. Draw the inequality x < 4 on the blank number line below.
1. Find the area of a parallelogram with a base of 8 cm and a perpendicular height of 5 cm.
2. A bag holds counters that are either pink or green. P(pink) = 0.4. What is P(green)?
3. On the grid below, sketch any triangle that has an area of exactly 8 cm².
(Hint: ½ × base × height = 8. So base × height must equal 16!).
1. Solve the equation: 4(x - 1) = 2x + 6
2. A triangular prism has a cross-section area of 15 cm² and a length of 10 cm. Calculate the volume.
3. Convert 25 miles to kilometres.
Grade all 10 Exams here!
1: 2x + 6 = 14 → 2x = 8 → x = 4
2: Closed circle at 2, arrow pointing to the right (→).
3: The smallest integer greater than 5 is 6.
1: Area = ½(10 + 14) × 5 = ½(24) × 5 = 12 × 5 = 60 cm².
2 & 3: Any rectangle drawn where length × width = 12. Example: Base = 4 cm (4 dots), Height = 3 cm (3 dots). Or 6x2.
1: Total counters = 5. P(red) = 3/5.
2: Cross ('X') placed exactly at 0.5 (Even chance) in the middle of the line.
3: 1.00 - 0.15 = 0.85
1: Volume = 5 × 4 × 10 = 200 cm³.
2: A net drawn with 6 squares (like a cross or 'T' shape).
3: Area of a square = 3 × 3 = 9 cm².
1: 2n ≥ 20
2: 3x < 10 + 2 → 3x < 12 → x < 4.
3: The circle is open at 1, pointing left, so the inequality is x < 1.
1: 40 ÷ 8 = 5. 5 × 5 = 25 miles.
2: 5x - 2x = 17 - 2 → 3x = 15 → x = 5.
1: 20 successes / 50 total. Fraction is 20/50, which simplifies to 2/5.
2: Exactly 1 out of the 4 sections in the circle should be shaded.
3: Not fair. The experimental probability is 30/60 (1/2), which is way higher than the theoretical probability (1/6).
1: x + 2x + 90 = 180 → 3x + 90 = 180 → 3x = 90 → x = 30.
2: Open circle at 4, arrow pointing to the left (←).
1: Area = base × height = 8 × 5 = 40 cm².
2: 1.0 - 0.4 = 0.6.
3: Any triangle where base × height = 16. Example: Base = 4 cm (4 dots), Height = 4 cm (4 dots).
1: 4x - 4 = 2x + 6 → 2x = 10 → x = 5.
2: Volume = 15 × 10 = 150 cm³.
3: 25 ÷ 5 = 5. 5 × 8 = 40 km.
You are a Math Queen, Ayosh!