Daily Practice · Higher Plus
August 1963 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1963 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1963
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1963On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 2nd August 1963Rationalise the denominator of 60/sqrt(5), giving your answer in its simplest form.
- 3rd August 1963Use the iteration x(n+1) = cube root of (8x(n) + 6) with x(0) = 4. Work out x(1) to 3 decimal places.
- 4th August 1963y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 5th August 1963In a vector proof you find that vector PQ = 2a + 6b and vector RS = 10a + 30b. What does this show about PQ and RS?
- 6th August 1963A bag holds 3 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 7th August 1963A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 3.5. How many values in total?
- 8th August 1963Simplify sqrt(50) + sqrt(72), giving your answer in the form a sqrt(b).
- 9th August 1963Work out the nth term of the quadratic sequence 8, 25, 50, 83, ...
- 10th August 1963y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 4.
- 11th August 1963A cuboid measures 6 cm by 8 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 12th August 1963A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 13th August 1963On 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?
- 14th August 1963A rectangle is 4 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 15th August 1963The point (6, -3) lies on y = f(x). Write down its image on y = f(x) - 1.
- 16th August 1963A train slows steadily from 25 m/s to rest in 10 seconds. Work out its deceleration.
- 17th August 1963A cuboid measures 11 cm by 9 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 18th August 1963A bag holds 5 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 19th August 1963A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 0.6. How many values in total?
- 20th August 1963Expand and simplify (9 + sqrt(7))(9 - sqrt(7)).
- 21st August 1963Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 22nd August 1963y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
- 23rd August 1963The 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.
- 24th August 1963A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 25th August 1963On 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?
- 26th August 1963A block has mass 730 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 27th August 1963f(x) = 4x - 6 and g(x) = 3x + 8. Work out fg(6).
- 28th August 1963y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 29th August 1963In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 30th August 1963The probability of winning a game is 3/4. A player expects 42 wins. How many games did they play?
- 31st August 1963A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?