Daily Practice · Higher Plus
January 1996 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1996 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1996
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1996y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 4.
- 2nd January 1996The 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.
- 3rd January 1996A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 6/11. Work out r.
- 4th January 1996On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 5th January 1996Rationalise the denominator of 30/sqrt(3), giving your answer in its simplest form.
- 6th January 1996The point (4, -5) lies on y = f(x). Write down its image on y = f(x - 1).
- 7th January 1996A train slows steadily from 30 m/s to rest in 4 seconds. Work out its deceleration.
- 8th January 1996In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 9th January 1996The probability of winning a game is 3/4. A player expects 36 wins. How many games did they play?
- 10th January 1996A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
- 11th January 1996Simplify sqrt(50) + sqrt(32), giving your answer in the form a sqrt(b).
- 12th January 1996Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 13th January 1996y is inversely proportional to x^2. When x = 3, y = 50. Work out y when x = 5.
- 14th January 1996In a vector proof you find that vector PQ = 4a - 3b and vector RS = 12a - 9b. What does this show about PQ and RS?
- 15th January 1996A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 16th January 1996On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 17th January 1996A rectangle is 28 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 18th January 1996f(x) = 4x - 5 and g(x) = 6x - 2. Work out fg(2).
- 19th January 1996y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 5.
- 20th January 1996A cuboid measures 11 cm by 3 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st January 1996A bag holds 6 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 22nd January 1996A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 3. How many values in total?
- 23rd January 1996Expand and simplify (4 + sqrt(5))(4 - sqrt(5)).
- 24th January 1996The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 25th January 1996y is directly proportional to sqrt(x). When x = 4, y = 8. Work out y when x = 81.
- 26th January 1996A cuboid measures 7 cm by 11 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th January 1996A bag holds 4 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th January 1996On 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?
- 29th January 1996A block has mass 610 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 30th January 1996A quadratic sequence starts 6, 24, 52, 90. Work out the second difference, and the coefficient of n^2.
- 31st January 1996A train slows steadily from 40 m/s to rest in 8 seconds. Work out its deceleration.