Daily Practice · Higher Plus
June 1997 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 1997, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
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The batch download puts all 5 tiers' June 1997 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1997
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1997In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 2nd June 1997The probability of winning a game is 3/5. A player expects 66 wins. How many games did they play?
- 3rd June 1997On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th June 1997A rectangle is 15 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 5th June 1997Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 6th June 1997y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 7th June 1997In a vector proof you find that vector PQ = 2a - 5b and vector RS = 10a - 25b. What does this show about PQ and RS?
- 8th June 1997A bag holds 6 red and n blue counters. The probability of taking a red is 6/13. Work out n.
- 9th June 1997A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
- 10th June 1997Expand and simplify (5 + sqrt(11))(5 - sqrt(11)).
- 11th June 1997f(x) = 6x + 7 and g(x) = 5x + 2. Work out fg(-3).
- 12th June 1997y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 16.
- 13th June 1997A cuboid measures 10 cm by 7 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th June 1997A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th June 1997On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 16th June 1997A block has mass 310 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 17th June 1997The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 18th June 1997A train slows steadily from 39 m/s to rest in 5 seconds. Work out its deceleration.
- 19th June 1997A cuboid measures 4 cm by 14 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th June 1997A bag holds 5 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st June 1997A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
- 22nd June 1997x = 62 and y = 14, each correct to the nearest whole number. Work out the upper bound of x - y.
- 23rd June 1997A quadratic sequence starts 0, 13, 36, 69. Work out the second difference, and the coefficient of n^2.
- 24th June 1997y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 2.
- 25th June 1997The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 26th June 1997A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 14/33. Work out r.
- 27th June 1997On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 28th June 1997A car covers 120 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 29th June 1997Solve x^2 + 8x + 7 > 0.
- 30th June 1997y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.