Daily Practice · Higher Plus
January 1963 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1963 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1963
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1963In 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.
- 2nd January 1963The probability of winning a game is 3/8. A player expects 18 wins. How many games did they play?
- 3rd January 1963A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?
- 4th January 1963Rationalise the denominator of 48/sqrt(6), giving your answer in its simplest form.
- 5th January 1963Solve x^2 + y^2 = 625 and y = x + 17 simultaneously.
- 6th January 1963y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 81.
- 7th January 1963In a vector proof you find that vector PQ = 6a - 5b and vector RS = 30a - 25b. What does this show about PQ and RS?
- 8th January 1963A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 9th January 1963On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 10th January 1963Simplify sqrt(32) + sqrt(8), giving your answer in the form a sqrt(b).
- 11th January 1963Use the iteration x(n+1) = cube root of (8x(n) + 2) with x(0) = 4. Work out x(1) to 3 decimal places.
- 12th January 1963A train slows steadily from 17 m/s to rest in 8 seconds. Work out its deceleration.
- 13th January 1963A cuboid measures 5 cm by 6 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th January 1963A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th January 1963A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 1.4. How many values in total?
- 16th January 1963A rectangle is 19 cm by 8 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th January 1963Work out the nth term of the quadratic sequence -5, -3, 1, 7, ...
- 18th January 1963y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 19th January 1963A cuboid measures 6 cm by 6 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th January 1963A bag holds 4 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st January 1963On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 22nd January 1963Expand and simplify (6 + sqrt(10))(6 - sqrt(10)).
- 23rd January 1963The point (3, 3) lies on y = f(x). Write down its image on y = f(x) + 6.
- 24th January 1963y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 25th January 1963The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 26th January 1963A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 21/55. Work out r.
- 27th January 1963A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 3.5. How many values in total?
- 28th January 1963A block has mass 640 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 29th January 1963Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 30th January 1963y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 81.
- 31st January 1963In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.