Daily Practice · Higher Plus
August 2002 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2002, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2002 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2002
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2002Simplify sqrt(18) + sqrt(98), giving your answer in the form a sqrt(b).
- 2nd August 2002In an algebraic proof, how would you write three consecutive integers in terms of an integer n?
- 3rd August 2002A train slows steadily from 19 m/s to rest in 8 seconds. Work out its deceleration.
- 4th August 2002In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 5th August 2002The probability of winning a game is 4/5. A player expects 28 wins. How many games did they play?
- 6th August 2002A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 0.6. How many values in total?
- 7th August 2002A rectangle is 13 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 8th August 2002Make x the subject of 6x + 5 = y(x + 5).
- 9th August 2002y is inversely proportional to x^2. When x = 2, y = 27. Work out y when x = 3.
- 10th August 2002In a vector proof you find that vector PQ = a + 2b and vector RS = 4a + 8b. What does this show about PQ and RS?
- 11th August 2002A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 12th August 2002On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 13th August 2002Expand and simplify (4 + sqrt(3))(4 - sqrt(3)).
- 14th August 2002Write 5/(x - 6) + 3/(x + 6) as a single fraction.
- 15th August 2002y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 5.
- 16th August 2002A cuboid measures 6 cm by 10 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th August 2002A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th August 2002A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 3.5. How many values in total?
- 19th August 2002A block has mass 770 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 20th August 2002Solve 20x^2 - 7x - 3 = 0.
- 21st August 2002y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 16.
- 22nd August 2002A cuboid measures 7 cm by 6 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd August 2002A bag holds 4 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th August 2002On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 25th August 2002x = 94 and y = 74, each correct to the nearest whole number. Work out the upper bound of x - y.
- 26th August 2002f(x) = 2x - 8. Work out the inverse function f^-1(x).
- 27th August 2002A train slows steadily from 32 m/s to rest in 4 seconds. Work out its deceleration.
- 28th August 2002The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 29th August 2002A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/21. Work out r.
- 30th August 2002A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 31st August 2002A car covers 210 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.