Daily Practice · Higher Plus
July 1974 5-a-day
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The batch download puts all 5 tiers' July 1974 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1974
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1974y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 2nd July 1974In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 3rd July 1974The probability of winning a game is 4/5. A player expects 56 wins. How many games did they play?
- 4th July 1974A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 0.8. How many values in total?
- 5th July 1974Rationalise the denominator of 12/sqrt(2), giving your answer in its simplest form.
- 6th July 1974The point (-1, -4) lies on y = f(x). Write down its image on y = f(-x).
- 7th July 1974y is directly proportional to sqrt(x). When x = 25, y = 30. Work out y when x = 4.
- 8th July 1974In a vector proof you find that vector PQ = 6a + 4b and vector RS = 18a + 12b. What does this show about PQ and RS?
- 9th July 1974A bag holds 4 red and n blue counters. The probability of taking a red is 4/9. Work out n.
- 10th July 1974On 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?
- 11th July 1974Simplify sqrt(18) + sqrt(8), giving your answer in the form a sqrt(b).
- 12th July 1974Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 13th July 1974A train slows steadily from 29 m/s to rest in 4 seconds. Work out its deceleration.
- 14th July 1974A cuboid measures 8 cm by 4 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th July 1974A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th July 1974A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 17th July 1974A rectangle is 10 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 18th July 1974f(x) = 2x - 8 and g(x) = 4x + 4. Work out fg(-1).
- 19th July 1974y is inversely proportional to x^2. When x = 5, y = 8. Work out y when x = 2.
- 20th July 1974A cuboid measures 7 cm by 14 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st July 1974A bag holds 6 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd July 1974On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 23rd July 1974Expand and simplify (3 + sqrt(7))(3 - sqrt(7)).
- 24th July 1974The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 25th July 1974y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 26th July 1974The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 27th July 1974A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
- 28th July 1974A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 29th July 1974A block has mass 400 g (to the nearest 10 g) and volume 13 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 30th July 1974A quadratic sequence starts -2, 5, 18, 37. Work out the second difference, and the coefficient of n^2.
- 31st July 1974y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 64.