Daily Practice · Higher Plus
April 1974 5-a-day
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The batch download puts all 5 tiers' April 1974 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1974
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1974Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 2nd April 1974y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 16.
- 3rd April 1974In 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.
- 4th April 1974The probability of winning a game is 1/2. A player expects 24 wins. How many games did they play?
- 5th April 1974On 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?
- 6th April 1974A car covers 150 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.
- 7th April 1974f(x) = 4x - 5 and g(x) = 2x - 4. Work out fg(2).
- 8th April 1974A train slows steadily from 32 m/s to rest in 5 seconds. Work out its deceleration.
- 9th April 1974In a vector proof you find that vector PQ = 6a + 6b and vector RS = 12a + 12b. What does this show about PQ and RS?
- 10th April 1974A bag holds 3 red and n blue counters. The probability of taking a red is 3/8. Work out n.
- 11th April 1974A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 0.6. How many values in total?
- 12th April 1974Rationalise the denominator of 99/sqrt(11), giving your answer in its simplest form.
- 13th April 1974The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 14th April 1974y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
- 15th April 1974A cuboid measures 7 cm by 10 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th April 1974A bag holds 10 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th April 1974On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 18th April 1974Simplify sqrt(32) + sqrt(98), giving your answer in the form a sqrt(b).
- 19th April 1974A quadratic sequence starts 4, 16, 36, 64. Work out the second difference, and the coefficient of n^2.
- 20th April 1974y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 21st April 1974A cuboid measures 14 cm by 13 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd April 1974A bag holds 5 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd April 1974A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 3. How many values in total?
- 24th April 1974A rectangle is 26 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 25th April 1974Solve x^2 - 3x + 2 < 0.
- 26th April 1974y is directly proportional to sqrt(x). When x = 4, y = 18. Work out y when x = 49.
- 27th April 1974The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 28th April 1974A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 29th April 1974On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 30th April 1974Expand and simplify (2 + sqrt(11))(2 - sqrt(11)).