Daily Practice · Higher Plus
June 1990 5-a-day
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The batch download puts all 5 tiers' June 1990 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1990
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1990y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 81.
- 2nd June 1990The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 3rd June 1990A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 5/14. Work out r.
- 4th June 1990On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 5th June 1990Expand and simplify (5 + sqrt(3))(5 - sqrt(3)).
- 6th June 1990The point (-3, -2) lies on y = f(x). Write down its image on y = f(x) + 1.
- 7th June 1990A train slows steadily from 32 m/s to rest in 4 seconds. Work out its deceleration.
- 8th June 1990In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 9th June 1990The probability of winning a game is 1/2. A player expects 28 wins. How many games did they play?
- 10th June 1990A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 0.6. How many values in total?
- 11th June 1990A block has mass 720 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 12th June 1990Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 13th June 1990y is inversely proportional to x^2. When x = 4, y = 27. Work out y when x = 3.
- 14th June 1990In a vector proof you find that vector PQ = 6a + 3b and vector RS = 24a + 12b. What does this show about PQ and RS?
- 15th June 1990A bag holds 3 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 16th June 1990On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 17th June 1990x = 163 and y = 64, each correct to the nearest whole number. Work out the upper bound of x - y.
- 18th June 1990f(x) = 4x - 7 and g(x) = 4x - 7. Work out fg(4).
- 19th June 1990y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 5.
- 20th June 1990A cuboid measures 13 cm by 13 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st June 1990A bag holds 5 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 22nd June 1990A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
- 23rd June 1990A car covers 670 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.
- 24th June 1990The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 25th June 1990y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 36.
- 26th June 1990A cuboid measures 8 cm by 13 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th June 1990A bag holds 6 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th June 1990On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 29th June 1990Rationalise the denominator of 22/sqrt(11), giving your answer in its simplest form.
- 30th June 1990A quadratic sequence starts 4, 12, 22, 34. Work out the second difference, and the coefficient of n^2.