Daily Practice · Higher Plus
July 2002 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2002, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2002 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2002
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2002A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 2nd July 2002Expand and simplify (3 + sqrt(2))(3 - sqrt(2)).
- 3rd July 2002A quadratic sequence starts 4, 11, 22, 37. Work out the second difference, and the coefficient of n^2.
- 4th July 2002y is directly proportional to sqrt(x). When x = 9, y = 12. Work out y when x = 81.
- 5th July 2002In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 6th July 2002The probability of winning a game is 3/4. A player expects 30 wins. How many games did they play?
- 7th July 2002On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 8th July 2002A block has mass 650 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 9th July 2002Solve x^2 - 8x + 12 > 0.
- 10th July 2002A train slows steadily from 40 m/s to rest in 5 seconds. Work out its deceleration.
- 11th July 2002In a vector proof you find that vector PQ = 6a - 4b and vector RS = 18a - 12b. What does this show about PQ and RS?
- 12th July 2002A bag holds 7 red and n blue counters. The probability of taking a red is 7/13. Work out n.
- 13th July 2002A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
- 14th July 2002x = 167 and y = 133, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th July 2002Write x^2 + 2x - 1 in the form (x + a)^2 + b.
- 16th July 2002y is inversely proportional to x^2. When x = 2, y = 25. Work out y when x = 5.
- 17th July 2002A cuboid measures 8 cm by 9 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th July 2002A bag holds 3 red and 11 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 19th July 2002On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 20th July 2002A car covers 290 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 21st July 2002Work out the coordinates of the turning point of y = x^2 + 2x - 3.
- 22nd July 2002y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 23rd July 2002A cuboid measures 8 cm by 13 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th July 2002A bag holds 6 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th July 2002A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
- 26th July 2002Rationalise the denominator of 18/sqrt(6), giving your answer in its simplest form.
- 27th July 2002Simplify (x^2 - 9x + 14)/(x - 2).
- 28th July 2002y is directly proportional to sqrt(x). When x = 25, y = 30. Work out y when x = 49.
- 29th July 2002The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 30th July 2002A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 31st July 2002On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?