Daily Practice · Higher Plus
May 1975 5-a-day
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The batch download puts all 5 tiers' May 1975 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1975
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1975Simplify sqrt(80) + sqrt(20), giving your answer in the form a sqrt(b).
- 2nd May 1975Work out the nth term of the quadratic sequence -7, -6, -1, 8, ...
- 3rd May 1975y is inversely proportional to x^2. When x = 3, y = 12. Work out y when x = 2.
- 4th May 1975In a vector proof you find that vector PQ = a + 4b and vector RS = 4a + 16b. What does this show about PQ and RS?
- 5th May 1975A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 6th May 1975On 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?
- 7th May 1975A rectangle is 21 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 8th May 1975The point (1, 4) lies on y = f(x). Write down its image on y = f(-x).
- 9th May 1975y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 10th May 1975A cuboid measures 10 cm by 9 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th May 1975A bag holds 4 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th May 1975A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 13th May 1975Expand and simplify (7 + sqrt(11))(7 - sqrt(11)).
- 14th May 1975Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 15th May 1975y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 81.
- 16th May 1975A cuboid measures 8 cm by 6 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th May 1975A bag holds 4 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th May 1975On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 19th May 1975A block has mass 750 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 20th May 1975f(x) = 5x - 8 and g(x) = 2x + 3. Work out fg(-1).
- 21st May 1975A train slows steadily from 29 m/s to rest in 10 seconds. Work out its deceleration.
- 22nd May 1975The 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.
- 23rd May 1975A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 24th May 1975A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3. How many values in total?
- 25th May 1975x = 167 and y = 133, each correct to the nearest whole number. Work out the upper bound of x - y.
- 26th May 1975The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 27th May 1975y is inversely proportional to x^2. When x = 2, y = 100. Work out y when x = 5.
- 28th May 1975In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 29th May 1975The probability of winning a game is 7/10. A player expects 105 wins. How many games did they play?
- 30th May 1975On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 31st May 1975A car covers 500 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.