Daily Practice · Higher Plus
June 1973 5-a-day
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The batch download puts all 5 tiers' June 1973 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1973
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1973The 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.
- 2nd June 1973A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 15/28. Work out r.
- 3rd June 1973A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
- 4th June 1973A block has mass 250 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.
- 5th June 1973f(x) = 6x - 1 and g(x) = 3x + 5. Work out fg(-1).
- 6th June 1973y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
- 7th June 1973In 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.
- 8th June 1973The probability of winning a game is 1/2. A player expects 32 wins. How many games did they play?
- 9th June 1973On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 10th June 1973x = 137 and y = 55, each correct to the nearest whole number. Work out the upper bound of x - y.
- 11th June 1973The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 12th June 1973y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 13th June 1973In a vector proof you find that vector PQ = 4a + 4b and vector RS = 8a + 8b. What does this show about PQ and RS?
- 14th June 1973A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 15th June 1973A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 16th June 1973A car covers 420 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 17th June 1973A quadratic sequence starts -1, 11, 33, 65. Work out the second difference, and the coefficient of n^2.
- 18th June 1973y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 49.
- 19th June 1973A cuboid measures 10 cm by 8 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th June 1973A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st June 1973On 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?
- 22nd June 1973Rationalise the denominator of 6/sqrt(2), giving your answer in its simplest form.
- 23rd June 1973Solve x^2 - 7x + 12 < 0.
- 24th June 1973A train slows steadily from 20 m/s to rest in 4 seconds. Work out its deceleration.
- 25th June 1973A cuboid measures 12 cm by 6 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th June 1973A bag holds 6 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th June 1973A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 0.8. How many values in total?
- 28th June 1973Simplify sqrt(27) + sqrt(75), giving your answer in the form a sqrt(b).
- 29th June 1973Write x^2 - 8x - 7 in the form (x + a)^2 + b.
- 30th June 1973y is inversely proportional to x^2. When x = 3, y = 50. Work out y when x = 5.